⊛
Summary

Model Violation

Overview Per-sequence detail

Gauge Invariant Error Metrics

Overview Germs Detail

Gauge Dependent Error Metrics

Overview Raw Estimates Gate Decompositions Gate Error Generators

For Reference

Input Reference System Reference
Help
G-Opt Param Value
0: Metric for gate-to-targetfrobenius
0: Metric for SPAM-to-targetfrobenius
0: Item weightsgates=1, spam=0
0: Gauge groupUnitary
1: SPAM penalty factor1.0
1: Metric for gate-to-targetfrobenius
1: Metric for SPAM-to-targetfrobenius
1: Item weightsgates=0, spam=1
1: Gauge groupTP Spam
G-Opt Param Value
0: Metric for gate-to-targetfrobenius
0: Metric for SPAM-to-targetfrobenius
0: Item weightsgates=1, spam=0
0: Gauge groupUnitary
1: SPAM penalty factor1.0
1: Metric for gate-to-targetfrobenius
1: Metric for SPAM-to-targetfrobenius
1: Item weightsgates=0, spam=1
1: Gauge groupTP Spam
G-Opt Param Value
0: Metric for gate-to-targetfrobenius
0: Metric for SPAM-to-targetfrobenius
0: Item weightsgates=1, spam=0
0: Gauge groupUnitary
1: SPAM penalty factor1.0
1: Metric for gate-to-targetfrobenius
1: Metric for SPAM-to-targetfrobenius
1: Item weightsgates=0, spam=1
1: Gauge groupTP Spam

Summary

Welcome to a pyGSTi analysis report! This report is organized into tabs, each of which is accessible from the sidebar on the left. This Summary tab summarizes the most popular analyses and figures of merit. Much more detailed analysis is available on other tabs. If this report encapsulates multiple datasets, estimates, or gauges, then you can switch between those using the dropdown menus on the sidebar. For more information about how to use this report, click on the Help tab link to the left.

Model violation summary. This figure is about goodness-of-fit. It indicates how well each of the estimates contained in this report fits its corresponding data. PyGSTi finds the maximum value of the loglikelihood (-2\log\mathrm{Pr(data|gateset)}), and compares it to what we expect to see if the data were generated by a Markovian gateset. In this plot, each bar or box shows by how many standard deviations the actual log-likelihood exceeds its expected value. Expected values and standard deviations are derived from \chi^2 theory. Low values indicate better fits (less model violation).
Model violation per iteration. This figure is about goodness-of-fit. This plot shows how well this estimate fits the data. PyGSTi finds the maximum value of the loglikelihood (-2\log\mathrm{Pr(data|gateset)}), and compares it to what we expect to see if the data were generated by a Markovian gateset. In this plot, each bar shows by how many standard deviations the actual log-likelihood exceeds its expected value. Expected values and standard deviations are derived from \chi^2 theory. On the horizontal axis, L indexes different ML estimates based on datasets including only circuits of length up to L. Low values indicate better fits (less model violation). Each bar is colored according to the star rating shown in the Model Violation tab.
Histogram of per-circuit model violation. This figure is about goodness-of-fit. When the estimate doesn't fit the data perfectly, we can quantify how well it fails to predict each individual circuit in the dataset, using the excess loglikelihood (-2\log\mathrm{Pr}(\mathrm{data}|\mathrm{gateset})) above and beyond the minimum value (-2 \log \mathrm{Pr}(\mathrm{data}|\mathrm{observed\ frequencies})). This plot shows a histogram of the those values for all the circuits in the dataset. Ideally, they should have the \chi^2 distribution shown by the solid line. Red indicates data that are inconsistent with the model at the 0.95 confidence level, as shown in more detail in the Model Violation tab.
Comparison of estimated gates to targets. This table is about gate error metrics (fidelity). The metrics in this table compare the estimated gates to their ideal counterparts, and can generally be interpreted as some kind of error rate (per gate use). Entanglement (process) fidelity and 1/2-diamond norm are the best known of these; they are the same for purely stochastic errors, but coherent errors contribute much more to diamond norm. 1/2-trace-distance is a proxy for diamond norm that doesn't require cvxPy to be installed. The Eigenvalue metrics are gauge-invariant versions of fidelity and diamond-norm that only depend on the gate itself (not its relationship to other gates). Hovering the pointer over a heading will pop up a description.
Gate Entanglement Infidelity 1/2 Trace Distance 1/2 Diamond-Dist Eigenvalue Ent. Infidelity Eigenvalue 1/2 Diamond-Dist
[]0.004518 ± 0.0033540.008601 ± 0.0152550.010213 ± 0.0240670.004518 ± 0.0033540.014303 ± 0.005622
Gxpi2:10.004066 ± 0.003330.008238 ± 0.0087640.011578 ± 0.0166540.004042 ± 0.0033230.007118 ± 0.012143
Gxpi2:00.00576 ± 0.0035170.020257 ± 0.0088290.027131 ± 0.0237170.005686 ± 0.0035150.036384 ± 0.016394
Gypi2:10.006353 ± 0.0048230.016997 ± 0.0088890.024357 ± 0.0252270.006272 ± 0.0047860.023633 ± 0.016052
Gypi2:00.010279 ± 0.0043810.026744 ± 0.0116630.035214 ± 0.0445430.010169 ± 0.0043790.044374 ± 0.023966
Gcphase:0:10.023373 ± 0.0064430.044264 ± 0.0070590.061999 ± 0.038090.023202 ± 0.0064450.080889 ± 0.009068
Gate Entanglement Infidelity 1/2 Trace Distance 1/2 Diamond-Dist Eigenvalue Ent. Infidelity Eigenvalue 1/2 Diamond-Dist
[]0.008327 ± 0.0041180.013126 ± 0.1130070.015144 ± 0.0136370.008327 ± 0.0041180.022465 ± 0.050942
Gxpi2:10.009474 ± 0.0037280.01249 ± 0.0058670.014506 ± 0.039510.009442 ± 0.0037140.016893 ± 0.00917
Gxpi2:00.008635 ± 0.0065250.026421 ± 0.0073590.034333 ± 0.0436410.008543 ± 0.0064990.052543 ± 0.015301
Gypi2:10.010377 ± 0.0070770.02524 ± 0.0074160.031271 ± 0.0164470.010279 ± 0.0070860.036754 ± 0.054848
Gypi2:00.010939 ± 0.0050130.028377 ± 0.0166110.036155 ± 0.0028750.010826 ± 0.0049190.054397 ± 0.026701
Gcphase:0:10.018755 ± 0.0051380.042103 ± 0.0056520.048942 ± 0.0472350.018634 ± 0.0052140.077814 ± 0.048129
Gate Entanglement Infidelity 1/2 Trace Distance 1/2 Diamond-Dist Eigenvalue Ent. Infidelity Eigenvalue 1/2 Diamond-Dist
[]00000
Gxpi2:100000
Gxpi2:000000
Gypi2:100000
Gypi2:000000
Gcphase:0:100000

Model Violation Analysis

The plots and tables on this tab summarize how well the GST estimate actually fits the data. Although they may be less familiar to you than, say, process fidelity, these analyses are essential to understanding the GST estimate, and how much to trust it! Real qubit systems often display behavior that isn't consistent with modeling each gate as a stationary CPTP map. When pyGSTi tries to fit such data to its model (a single gateset), this "non-Markovianity" manifests as model violation. This tab provides several views of the model violation observed for this fit, ranging from the coarse-grained (total violation) to hyper-detailed (per-circuit violation). More observed model violation ⇒ the error metrics on other tabs should be trusted less.

Model violation summary. This plot summarizes how well GST was able to fit the data -- or subsets of it -- to a gateset. Bars indicate the difference between the actual and expected log-likelihood values, and are given in units of standard deviations of the appropriate \chi^2 distribution. Each bar corresponds to a subset of the data including only circuits of length up to \sim L; the rightmost bar corresponds to the full dataset. Low values are better (less model violation), and bars are colored according to the star rating found in a later table detailing the overall model violation.
Detailed overall model violation. This table provides a detailed look at how the observed model violation -- defined by how badly the GST model fits the data -- evolves as more and more of the data are incorporated into the fit. PyGSTi fits the data iteratively, starting by just fitting data from the shortest circuits (L=1), and then adding longer and longer sequences. Each subset of the data, defined by its maximum sequence length L, yields an independent fit that is analyzed here. The key quantity is the difference between the observed and expected maximum loglikelihood (\log(\mathcal{L})). If the model fits, then 2\Delta\log(\mathcal{L}) should be a \chi^2_k random variable, where k (the degrees of freedom) is the difference between N_S (the number of independent data points) and N_p (the number of model parameters). So 2\Delta\log(\mathcal{L}) should lie in [k-\sqrt{2k},k+\sqrt{2k}], and N_\sigma = (2\Delta\log(\mathcal{L})-k)/\sqrt{2k} quantifies how many standard deviations it falls above the mean (a p-value can be straightforwardly derived from N_\sigma). The rating from 1 to 5 stars gives a very crude indication of goodness of fit. Heading tool tips provide descriptions of each column's value.
L 2Δ(log L) k 2Δ(log L)-k √2k Nsigma Ns Np Rating
12342.02411251217.02447.4341625.723881263★★★
23104.19216691435.19257.7754324.829311262★★★
44525.09626331892.09672.5672126.138881255★★★
86629.96938502779.96987.7496431.751061256★★★
L 2Δ(log L) k 2Δ(log L)-k √2k Nsigma Ns Np Rating
15713.00921693544.00965.863553.82388219★★★
27080.58927134367.58973.6613959.32931218★★★
49545.76836715874.76885.6854768.63888217★★★
813590.5748928698.57398.914187.95106214★★★
L 2Δ(log L) k 2Δ(log L)-k √2k Nsigma Ns Np Rating
1303924.22214301710.266.543225×1032388174★
2387138.12757384381.174.256315×1032931174★
4537975.43714534261.486.185856×1033888174★
8737897.64932732965.699.317677×1035106174★
Per-circuit model violation vs. circuit length The fit's total 2\Delta\log(\mathcal{L}) is a sum over all N_s circuits used for GST. This plot shows 2\Delta\log(\mathcal{L}) for each individual circuit, plotted against that circuit's length (on the X axis). Certain forms of non-Markovian noise, like slow drift, produce a characteristic linear relationship. Note that the length plotted here is the actual length of the circuit, not its nominal L.

Model violation for each individual circuit

This tab presents the second of two statistical tests available to detect that a dataset violates pyGSTi's Markovian gateset model. The first is based on the aggregate loglikelihood score presented elsewhere. This tab shows the individual loglikelihood scores for each circuit in the dataset. Each circuit is represented by a colored box, whose color indicates how badly this estimate (model) failed to predict the observed outcome frequencies of that circuit. Light gray indicates consistency with the model, dark gray indicates possible -- but statistically insignificant -- inconsistency, and red squares indicate circuits whose outcomes are inconsistent with the model at the family-wise 95 percent confidence level. In other words, if data are generated by a Markovian gateset, then with 95%% probability every box will be gray. Even a single red square thus represents a clear detection of model violation. When many squares are red, their pattern can provide useful diagnostic clues to what kind of non-Markovian noise is present.

Per-sequence model violation box plot. This plot shows the 2\Delta\log(\mathcal{L}) contribution for each individual circuit in the dataset. Each box represents a single gate sequence, and its color indicates whether GST was able to fit the corresponding frequency well. Shades of white/gray indicate typical (within the expected) values. Red squares represent statistically significant evidence for model violation (non-Markovianity), and the probabilty that any red squares appear is 5% when the data really are Markovian. Each square block of pixels (plaquette) corresponds to a particular germ-power "base sequence", and each pixel within a block corresponds to a specific "fiducial pair" -- i.e., choice of pre- and post-fiducial sequences. The base sequences are arranged by germ (varying from row to row), and by power/length (varying from column to column). Hovering over a colored box will pop up the exact circuit to which it corresponds, the observed frequencies, and the corresponding probabilities predicted by the GST estimate of the gateset. The slider below the figure permits switching between different estimates, labeled by L, which were obtained from subsets of the data that included only base sequences of length up to L.
Per-sequence total variational distance box plot. This plot shows the total variational distance (\frac{1}{2}\sum_i|p_i-f_i|) contribution for each individual circuit in the dataset. Each box represents a single gate sequence, and its color indicates how well the observed frequency matches the probability generated by GST's best-estimate gate set. Each square block of pixels (plaquette) corresponds to a particular germ-power "base sequence", and each pixel within a block corresponds to a specific "fiducial pair" -- i.e., choice of pre- and post-fiducial sequences. The base sequences are arranged by germ (varying from row to row), and by power/length (varying from column to column). Hovering over a colored box will pop up the exact circuit to which it corresponds, the observed frequencies, and the corresponding probabilities predicted by the GST estimate of the gateset. The slider below the figure permits switching between different estimates, labeled by L, which were obtained from subsets of the data that included only base sequences of length up to L.

Gauge Invariant Error Metrics

GST can estimate gates up to an overall gauge. PyGSTi tries to find a good gauge in which to report process matrices and gauge-variant metrics like fidelity -- but sometimes this goes wrong. The most reliable error metrics and gate properties are gauge-invariant ones, and these are listed on this tab.

RB error metrics This table shows estimates for the error rate that would be obtained using two different Randomized Benchmarking (RB) protocols . The Clifford RB number corresponds to the most standard form of RB, Clifford RB (CRB), where random Clifford gate sequences are performed. This number is dependent on how the Clifford operations are compiled into the primitive gates, and so if you didn't specify a Clifford compilation and pygsti couldn't deduce one, this quantity will be absent. Note that this is the error rate per-Clifford; it has not been rescaled to a per-primitive error rate. The primitive RB number corresponds to performing RB on random sequences of the primitive gates, rather than the Cliffords, which is known as Direct RB (DRB). DRB allows for sampling layers of primitives according to a general probability distribution over the primitive gates; the number reported here corresponds to uniformly sampling the primitive gates. This number does not require any compilation table and is always be computed by pyGSTi. Two caveats regarding these RB numbers: 1) The primitive RB number is not meaningful for arbitrary gate sets; if the gate set generates the Clifford group or it is a universal gate set then it is definitely meaningful, modulo the second caveat. 2) These predicted RB numbers rely on a perturbative technique, and if the estimated gates are far from their ideal counterparts the predicted numbers may be very inaccurate (and the empirical RB error rate itself may even be ill-defined: the RB decay could be non-exponential). For both of these RB protocols there is also more than one definition of the RB number, as a function of the p obtained from fitting RB data to A + Bp^m. Here we use the definition r = (4^n - 1)(1-p)/4^n for an n-qubit gate set, which means that r = entanglement infidelity = 1/2 diamond distance if there are uniform depolarizing errors on all the gates (where these two quantities are w.r.t. the gate set benchmarked, so the Clifford gates for CRB and the primitive gates for DRB). For more general errors, these first two quantities will often be roughly equal, although that is not guaranteed. Note that these numbers should not be directly compared to RB numbers derived using the commonly-used alternative formula r = (2^n - 1)(1-p)/2^n (which is related to average gate infidelity, rather than entanglement infidelity).
Metric Value
Predicted primitive RB number-1 ± 0
Metric Value
Predicted primitive RB number-1 ± 0
Metric Value
Predicted primitive RB number-1
SPAM probabilities This table shows estimated SPAM probabilities for each measurement outcome. These are computed as \mathrm{Tr}[\rho E_i], where \rho is an estimated initial state (often labelled \rho_0), and \{E_i\} is the estimated n-outcome POVM. The symbol E_C denotes the nth POVM effect, which is not allowed to vary freely but is defined by subtracting the sum of the other effects (which are freely varied) from the identity.
00 01 10 11
Target ρ01000
Estimated ρ00.939965 ± 0.0057930.036672 ± 0.0047310.021212 ± 0.0038360.002151 ± 0.002117
00 01 10 11
Target ρ01000
Estimated ρ00.868819 ± 0.0069960.056221 ± 0.0057660.059755 ± 0.0059810.015205 ± 0.004949
00 01 10 11
Target ρ01000
Estimated ρ01000
Gram matrix spectrum. The GST Gram matrix is not a standard error metric, but it is gauge-invariant and critical to the GST process. It provides some insight into generalized SPAM. It is the (estimated) matrix of inner products between all the input states prepared by the various preparation fiducials, and all the measured effects prepared by the various measurement fiducials. LGST involves inverting the Gram matrix, so it needs to be full rank. In the plot, each pair of bars shows the nth eigenvalues of the estimated Gram matrix and the Gram matrix predicted by the ideal targets (respectively). Larger eigenvalues indicate better sensitivity, and the number of non-zero values indicates the dimension of the state (density matrix) space being probed (e.g., for a single qubit, the Gram matrix should have 4 O(1) eigenvalues).
Spectral error metrics between estimated gates and ideal targets This table presents a variety of gauge-invariant quantities that quantify the distance or discrepancy between (1) an estimated gate, and (2) the ideal corresponding target operation. Each of these error metrics depends only on a specific gate's spectrum (eigenvalues), which are gauge-invariant and non-relational (i.e., they pertain to a single gate). Hovering over a column header will pop up a mathematical description of the corresponding metric.
Gate Eigenvalue Ent. Infidelity Eigenvalue Avg. Gate Infidelity Eigenvalue Non-U. Ent. Infidelity Eigenvalue Non-U. Avg. Gate Infidelity Eigenvalue 1/2 Diamond-Dist Eigenvalue Non-U. 1/2 Diamond-Dist
[]0.0045180.0036150.0044850.0035880.0143030.006135
Gxpi2:10.0040420.0032340.0040350.0032280.0071180.007118
Gxpi2:00.0056860.0045490.0054420.0043530.0363840.008071
Gypi2:10.0062720.0050170.0061720.0049380.0236330.009257
Gypi2:00.0101690.0081350.0097640.0078110.0443740.016027
Gcphase:0:10.0232020.0185620.0223920.0179140.0808890.039705
Gate Eigenvalue Ent. Infidelity Eigenvalue Avg. Gate Infidelity Eigenvalue Non-U. Ent. Infidelity Eigenvalue Non-U. Avg. Gate Infidelity Eigenvalue 1/2 Diamond-Dist Eigenvalue Non-U. 1/2 Diamond-Dist
[]0.0083270.0066620.0082580.0066060.0224650.013276
Gxpi2:10.0094420.0075540.0094420.0075540.0168930.016865
Gxpi2:00.0085430.0068350.008140.0065120.0525430.010909
Gypi2:10.0102790.0082230.0100020.0080020.0367540.015572
Gypi2:00.0108260.0086610.0103410.0082730.0543970.015888
Gcphase:0:10.0186340.0149070.0176780.0141430.0778140.030349
Gate Eigenvalue Ent. Infidelity Eigenvalue Avg. Gate Infidelity Eigenvalue Non-U. Ent. Infidelity Eigenvalue Non-U. Avg. Gate Infidelity Eigenvalue 1/2 Diamond-Dist Eigenvalue Non-U. 1/2 Diamond-Dist
[]000000
Gxpi2:1000000
Gxpi2:0000000
Gypi2:1000000
Gypi2:0000000
Gcphase:0:1000000
Single metric comparison. TODO: caption
Eigenvalue Ent. Infidelity
Gate CPTP H+S Target
[]0.0045180.0083270
Gxpi2:10.0040420.0094420
Gxpi2:00.0056860.0085430
Gypi2:10.0062720.0102790
Gypi2:00.0101690.0108260
Gcphase:0:10.0232020.0186340
Eigenvalue Avg. Gate Infidelity
Gate CPTP H+S Target
[]0.0036150.0066620
Gxpi2:10.0032340.0075540
Gxpi2:00.0045490.0068350
Gypi2:10.0050170.0082230
Gypi2:00.0081350.0086610
Gcphase:0:10.0185620.0149070
Eigenvalue Non-U. Ent. Infidelity
Gate CPTP H+S Target
[]0.0044850.0082580
Gxpi2:10.0040350.0094420
Gxpi2:00.0054420.008140
Gypi2:10.0061720.0100020
Gypi2:00.0097640.0103410
Gcphase:0:10.0223920.0176780
Eigenvalue Non-U. Avg. Gate Infidelity
Gate CPTP H+S Target
[]0.0035880.0066060
Gxpi2:10.0032280.0075540
Gxpi2:00.0043530.0065120
Gypi2:10.0049380.0080020
Gypi2:00.0078110.0082730
Gcphase:0:10.0179140.0141430
Eigenvalue 1/2 Diamond-Dist
Gate CPTP H+S Target
[]0.0143030.0224650
Gxpi2:10.0071180.0168930
Gxpi2:00.0363840.0525430
Gypi2:10.0236330.0367540
Gypi2:00.0443740.0543970
Gcphase:0:10.0808890.0778140
Eigenvalue Non-U. 1/2 Diamond-Dist
Gate CPTP H+S Target
[]0.0061350.0132760
Gxpi2:10.0071180.0168650
Gxpi2:00.0080710.0109090
Gypi2:10.0092570.0155720
Gypi2:00.0160270.0158880
Gcphase:0:10.0397050.0303490
Gauge-robust gate metrics. This table gives gauge-robust metrics indicating the intrinsic errors on a gate due to its eigenvalues not being perfect (the diagonal elements) and the relational errors between pairs of gates, due to having imperfect eigenspaces.
Blank
Eigenvalues of estimated gates. This table lists the spectrum of each estimated gate. It also breaks out the real and imaginary parts of each eigenvalue, and it compares the estimated eigenvalues to those of the ideal target gates in several useful ways. To do these comparisons, each estimated eigenvalue needs to be matched up with a target eigenvalue, and pyGSTi does this independently for each metric by computing a minimum-weight matching based on that metric. Hovering over a column header will pop up a mathematical description of the corresponding metric.
Gate Eigenvalues ($E$) Target Evals. ($T$) $|E - T|$ $1.0 - \mathrm{Re}(\bar{T}\cdot E)$ $\mathrm{Re} \log(E)$ $\mathrm{Im} \log(E)$ $|\mathrm{Re}(\log E) - \mathrm{Re}(\log T)|$ $|\mathrm{Im}(\log E) - \mathrm{Im}(\log T)|$
[]$ \begin{pmatrix} 1 \\ 0.996791 \\ 0.996531e^{i0.005\pi} \\ 0.996531e^{-i0.005\pi} \\ 0.995803e^{i0.002\pi} \\ 0.995803e^{-i0.002\pi} \\ 0.995384e^{i0.002\pi} \\ 0.995384e^{-i0.002\pi} \\ 0.99524e^{i0.004\pi} \\ 0.99524e^{-i0.004\pi} \\ 0.994699e^{i0.000\pi} \\ 0.994699e^{-i0.000\pi} \\ 0.994608e^{i0.001\pi} \\ 0.994608e^{-i0.001\pi} \\ 0.993456e^{i0.002\pi} \\ 0.993456e^{-i0.002\pi} \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.015809 \\ 0.033197e^{i0.127\pi} \\ 0.033197e^{i0.127\pi} \\ 0.06558e^{i0.106\pi} \\ 0.06558e^{i0.106\pi} \\ 0.08755e^{i0.308\pi} \\ 0.08755e^{i0.308\pi} \\ 0.047392e^{i0.128\pi} \\ 0.047392e^{i0.128\pi} \\ 0.088316e^{i0.181\pi} \\ 0.088316e^{i0.181\pi} \\ 0.104669e^{i0.227\pi} \\ 0.104669e^{i0.227\pi} \\ 0.082095e^{i0.329\pi} \\ 0.082095e^{i0.329\pi} \end{pmatrix} $ $ \begin{pmatrix} 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.003209 \\ 0.015257 \\ 0.015257 \\ 0.007848 \\ 0.007848 \\ 0.008827 \\ 0.008827 \\ 0.013092 \\ 0.013092 \\ 0.005341 \\ 0.005341 \\ 0.005993 \\ 0.005993 \\ 0.009735 \\ 0.009735 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.015809 \\ 0.033197 \\ 0.033197 \\ 0.06558 \\ 0.06558 \\ 0.08755 \\ 0.08755 \\ 0.047392 \\ 0.047392 \\ 0.088316 \\ 0.088316 \\ 0.104669 \\ 0.104669 \\ 0.082095 \\ 0.082095 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.003209 \\ 0.003579 \\ 0.003579 \\ 0.004219 \\ 0.004219 \\ 0.004645 \\ 0.004645 \\ 0.004834 \\ 0.004834 \\ 0.005301 \\ 0.005301 \\ 0.005396 \\ 0.005396 \\ 0.00657 \\ 0.00657 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.015809 \\ 0.0306 \\ 0.0306 \\ 0.06198 \\ 0.06198 \\ 0.049648 \\ 0.049648 \\ 0.043599 \\ 0.043599 \\ 0.074394 \\ 0.074394 \\ 0.07909 \\ 0.07909 \\ 0.042094 \\ 0.042094 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ -0.003214 \\ -0.003475 \\ -0.003475 \\ -0.004206 \\ -0.004206 \\ -0.004627 \\ -0.004627 \\ -0.004771 \\ -0.004771 \\ -0.005315 \\ -0.005315 \\ -0.005407 \\ -0.005407 \\ -0.006566 \\ -0.006566 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.015735 \\ 0.030501 \\ 0.030139 \\ 0.060711 \\ 0.060458 \\ 0.051541 \\ 0.050554 \\ 0.043241 \\ 0.042822 \\ 0.073142 \\ 0.073088 \\ 0.078704 \\ 0.078395 \\ 0.044278 \\ 0.043338 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0.004737 \\ -0.004737 \\ 0.002115 \\ -0.002115 \\ 0.002401 \\ -0.002401 \\ 0.003891 \\ -0.003891 \\ 0.000208 \\ -0.000208 \\ 0.000835 \\ -0.000835 \\ 0.002301 \\ -0.002301 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0.003847 \\ 0.00413 \\ 0.006323 \\ 0.006572 \\ 0.021804 \\ 0.022054 \\ 0.005527 \\ 0.005856 \\ 0.014147 \\ 0.014177 \\ 0.020233 \\ 0.020362 \\ 0.021527 \\ 0.021735 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0.003214 \\ 0.003475 \\ 0.003475 \\ 0.004206 \\ 0.004206 \\ 0.004627 \\ 0.004627 \\ 0.004771 \\ 0.004771 \\ 0.005315 \\ 0.005315 \\ 0.005407 \\ 0.005407 \\ 0.006566 \\ 0.006566 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.015735 \\ 0.030501 \\ 0.030139 \\ 0.060711 \\ 0.060458 \\ 0.051541 \\ 0.050554 \\ 0.043241 \\ 0.042822 \\ 0.073142 \\ 0.073088 \\ 0.078704 \\ 0.078395 \\ 0.044278 \\ 0.043338 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0.004737 \\ 0.004737 \\ 0.002115 \\ 0.002115 \\ 0.002401 \\ 0.002401 \\ 0.003891 \\ 0.003891 \\ 0.000208 \\ 0.000208 \\ 0.000835 \\ 0.000835 \\ 0.002301 \\ 0.002301 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0.003847 \\ 0.00413 \\ 0.006323 \\ 0.006572 \\ 0.021804 \\ 0.022054 \\ 0.005527 \\ 0.005856 \\ 0.014147 \\ 0.014177 \\ 0.020233 \\ 0.020362 \\ 0.021527 \\ 0.021735 \end{pmatrix} $ π
Gxpi2:1$ \begin{pmatrix} 1 \\ 0.997483e^{i0.498\pi} \\ 0.997483e^{-i0.498\pi} \\ 0.997246e^{i0.499\pi} \\ 0.997246e^{-i0.499\pi} \\ 0.996617 \\ 0.996347 \\ 0.996066e^{i0.002\pi} \\ 0.996066e^{-i0.002\pi} \\ 0.995239e^{i0.002\pi} \\ 0.995239e^{-i0.002\pi} \\ 0.994789e^{i0.500\pi} \\ 0.994789e^{-i0.500\pi} \\ 0.994209e^{i0.501\pi} \\ 0.994209e^{-i0.501\pi} \\ 0.992407 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.013116e^{i0.286\pi} \\ 0.013116e^{i0.286\pi} \\ 0.012005e^{i0.190\pi} \\ 0.012005e^{i0.190\pi} \\ 0.036209 \\ 0.019967 \\ 0.025786e^{i0.090\pi} \\ 0.025786e^{i0.090\pi} \\ 0.024928e^{i0.343\pi} \\ 0.024928e^{i0.343\pi} \\ 0.011678e^{i0.195\pi} \\ 0.011678e^{i0.195\pi} \\ 0.013669e^{i0.278\pi} \\ 0.013669e^{i0.278\pi} \\ 0.012952 \end{pmatrix} $ $ \begin{pmatrix} 1 \\ 1i \\ -1i \\ 1i \\ -1i \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1i \\ -1i \\ 1i \\ -1i \\ 1 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.006895 \\ 0.006895 \\ 0.003185 \\ 0.003185 \\ 0.003383 \\ 0.003653 \\ 0.006167 \\ 0.006167 \\ 0.007136 \\ 0.007136 \\ 0.005224 \\ 0.005224 \\ 0.006774 \\ 0.006774 \\ 0.007593 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.013116 \\ 0.013116 \\ 0.012005 \\ 0.012005 \\ 0.036209 \\ 0.019967 \\ 0.025786 \\ 0.025786 \\ 0.024928 \\ 0.024928 \\ 0.011678 \\ 0.011678 \\ 0.013669 \\ 0.013669 \\ 0.012952 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.002538 \\ 0.002538 \\ 0.002756 \\ 0.002756 \\ 0.003383 \\ 0.003653 \\ 0.003946 \\ 0.003946 \\ 0.004775 \\ 0.004775 \\ 0.005211 \\ 0.005211 \\ 0.005797 \\ 0.005797 \\ 0.007593 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.008171 \\ 0.008171 \\ 0.009921 \\ 0.009921 \\ 0.036209 \\ 0.019967 \\ 0.024767 \\ 0.024767 \\ 0.011794 \\ 0.011794 \\ 0.009546 \\ 0.009546 \\ 0.008785 \\ 0.008785 \\ 0.012952 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ -0.00252 \\ -0.00252 \\ -0.002758 \\ -0.002758 \\ -0.003389 \\ -0.003659 \\ -0.003942 \\ -0.003942 \\ -0.004773 \\ -0.004773 \\ -0.005225 \\ -0.005225 \\ -0.005807 \\ -0.005807 \\ -0.007622 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.010317 \\ -0.01025 \\ 0.006821 \\ -0.006736 \\ 0.035688 \\ 0.019842 \\ 0.024618 \\ 0.024553 \\ 0.012133 \\ 0.011903 \\ 0.006788 \\ -0.006734 \\ 0.010485 \\ -0.010581 \\ 0.012967 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.497954 \\ -0.497954 \\ 0.499491 \\ -0.499491 \\ 0 \\ 0 \\ 0.001515 \\ -0.001515 \\ 0.001696 \\ -0.001696 \\ 0.499883 \\ -0.499883 \\ 0.501122 \\ -0.501122 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ -0.00256 \\ 0.002656 \\ -0.003142 \\ 0.003191 \\ 0 \\ 0 \\ 0.002201 \\ 0.002275 \\ 0.00692 \\ 0.006961 \\ -0.003033 \\ 0.003076 \\ -0.002795 \\ 0.00283 \\ 0 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0.00252 \\ 0.00252 \\ 0.002758 \\ 0.002758 \\ 0.003389 \\ 0.003659 \\ 0.003942 \\ 0.003942 \\ 0.004773 \\ 0.004773 \\ 0.005225 \\ 0.005225 \\ 0.005807 \\ 0.005807 \\ 0.007622 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.010317 \\ 0.01025 \\ 0.006821 \\ 0.006736 \\ 0.035688 \\ 0.019842 \\ 0.024618 \\ 0.024553 \\ 0.012133 \\ 0.011903 \\ 0.006788 \\ 0.006734 \\ 0.010485 \\ 0.010581 \\ 0.012967 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.002046 \\ 0.002046 \\ 0.000509 \\ 0.000509 \\ 0 \\ 0 \\ 0.001515 \\ 0.001515 \\ 0.001696 \\ 0.001696 \\ 0.000117 \\ 0.000117 \\ 0.001122 \\ 0.001122 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0.00256 \\ 0.002656 \\ 0.003142 \\ 0.003191 \\ 0 \\ 0 \\ 0.002201 \\ 0.002275 \\ 0.00692 \\ 0.006961 \\ 0.003033 \\ 0.003076 \\ 0.002795 \\ 0.00283 \\ 0 \end{pmatrix} $ π
Gxpi2:0$ \begin{pmatrix} 1 \\ 0.997502 \\ 0.996375e^{i0.503\pi} \\ 0.996375e^{-i0.503\pi} \\ 0.996167e^{i0.502\pi} \\ 0.996167e^{-i0.502\pi} \\ 0.995741 \\ 0.993843 \\ 0.993534e^{i0.512\pi} \\ 0.993534e^{-i0.512\pi} \\ 0.993398e^{i0.009\pi} \\ 0.993398e^{-i0.009\pi} \\ 0.992042e^{i0.010\pi} \\ 0.992042e^{-i0.010\pi} \\ 0.991391e^{i0.493\pi} \\ 0.991391e^{-i0.493\pi} \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.006834 \\ 0.009491e^{i0.149\pi} \\ 0.009491e^{i0.149\pi} \\ 0.010889e^{i0.135\pi} \\ 0.010889e^{i0.135\pi} \\ 0.005753 \\ 0.017147 \\ 0.035739e^{i0.334\pi} \\ 0.035739e^{i0.334\pi} \\ 0.018055e^{i0.326\pi} \\ 0.018055e^{i0.326\pi} \\ 0.038498e^{i0.377\pi} \\ 0.038498e^{i0.377\pi} \\ 0.030343e^{i0.369\pi} \\ 0.030343e^{i0.369\pi} \end{pmatrix} $ $ \begin{pmatrix} 1 \\ 1 \\ 1i \\ -1i \\ 1i \\ -1i \\ 1 \\ 1 \\ 1i \\ -1i \\ 1 \\ 1 \\ 1 \\ 1 \\ 1i \\ -1i \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.002498 \\ 0.010953 \\ 0.010953 \\ 0.007579 \\ 0.007579 \\ 0.004259 \\ 0.006157 \\ 0.03881 \\ 0.03881 \\ 0.029408 \\ 0.029408 \\ 0.031842 \\ 0.031842 \\ 0.02383 \\ 0.02383 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.006834 \\ 0.009491 \\ 0.009491 \\ 0.010889 \\ 0.010889 \\ 0.005753 \\ 0.017147 \\ 0.035739 \\ 0.035739 \\ 0.018055 \\ 0.018055 \\ 0.038498 \\ 0.038498 \\ 0.030343 \\ 0.030343 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.002498 \\ 0.003679 \\ 0.003679 \\ 0.003854 \\ 0.003854 \\ 0.004259 \\ 0.006157 \\ 0.007198 \\ 0.007198 \\ 0.007013 \\ 0.007013 \\ 0.008433 \\ 0.008433 \\ 0.008856 \\ 0.008856 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.006834 \\ 0.008473 \\ 0.008473 \\ 0.009919 \\ 0.009919 \\ 0.005753 \\ 0.017147 \\ 0.017759 \\ 0.017759 \\ 0.009373 \\ 0.009373 \\ 0.014459 \\ 0.014459 \\ 0.012147 \\ 0.012147 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ -0.002501 \\ -0.003632 \\ -0.003632 \\ -0.00384 \\ -0.00384 \\ -0.004269 \\ -0.006176 \\ -0.006487 \\ -0.006487 \\ -0.006624 \\ -0.006624 \\ -0.00799 \\ -0.00799 \\ -0.008646 \\ -0.008646 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.006828 \\ 0.004231 \\ -0.004353 \\ 0.004484 \\ -0.004535 \\ 0.005761 \\ 0.017106 \\ 0.030222 \\ -0.03225 \\ 0.009944 \\ 0.009068 \\ 0.01617 \\ 0.01401 \\ 0.027984 \\ -0.028072 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0.503296 \\ -0.503296 \\ 0.502085 \\ -0.502085 \\ 0 \\ 0 \\ 0.512221 \\ -0.512221 \\ 0.009152 \\ -0.009152 \\ 0.009854 \\ -0.009854 \\ 0.492896 \\ -0.492896 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ -0.002709 \\ 0.002704 \\ -0.003165 \\ 0.003175 \\ 0 \\ 0 \\ -0.005886 \\ 0.005478 \\ 0.004808 \\ 0.004984 \\ 0.01112 \\ 0.011427 \\ -0.003598 \\ 0.004215 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0.002501 \\ 0.003632 \\ 0.003632 \\ 0.00384 \\ 0.00384 \\ 0.004269 \\ 0.006176 \\ 0.006487 \\ 0.006487 \\ 0.006624 \\ 0.006624 \\ 0.00799 \\ 0.00799 \\ 0.008646 \\ 0.008646 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.006828 \\ 0.004231 \\ 0.004353 \\ 0.004484 \\ 0.004535 \\ 0.005761 \\ 0.017106 \\ 0.030222 \\ 0.03225 \\ 0.009944 \\ 0.009068 \\ 0.01617 \\ 0.01401 \\ 0.027984 \\ 0.028072 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0.003296 \\ 0.003296 \\ 0.002085 \\ 0.002085 \\ 0 \\ 0 \\ 0.012221 \\ 0.012221 \\ 0.009152 \\ 0.009152 \\ 0.009854 \\ 0.009854 \\ 0.007104 \\ 0.007104 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0.002709 \\ 0.002704 \\ 0.003165 \\ 0.003175 \\ 0 \\ 0 \\ 0.005886 \\ 0.005478 \\ 0.004808 \\ 0.004984 \\ 0.01112 \\ 0.011427 \\ 0.003598 \\ 0.004215 \end{pmatrix} $ π
Gypi2:1$ \begin{pmatrix} 1 \\ 0.996262 \\ 0.995668e^{i0.501\pi} \\ 0.995668e^{-i0.501\pi} \\ 0.994997e^{i0.005\pi} \\ 0.994997e^{-i0.005\pi} \\ 0.994226e^{i0.008\pi} \\ 0.994226e^{-i0.008\pi} \\ 0.99416e^{i0.494\pi} \\ 0.99416e^{-i0.494\pi} \\ 0.993345 \\ 0.991749 \\ 0.990751e^{i0.506\pi} \\ 0.990751e^{-i0.506\pi} \\ 0.990126e^{i0.499\pi} \\ 0.990126e^{-i0.499\pi} \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.011409 \\ 0.013921e^{i0.147\pi} \\ 0.013921e^{i0.147\pi} \\ 0.020085e^{i0.333\pi} \\ 0.020085e^{i0.333\pi} \\ 0.02497e^{i0.247\pi} \\ 0.02497e^{i0.247\pi} \\ 0.006584e^{i0.249\pi} \\ 0.006584e^{i0.249\pi} \\ 0.042272 \\ 0.038761 \\ 0.038939e^{i0.081\pi} \\ 0.038939e^{i0.081\pi} \\ 0.01071e^{i0.226\pi} \\ 0.01071e^{i0.226\pi} \end{pmatrix} $ $ \begin{pmatrix} 1 \\ 1 \\ 1i \\ -1i \\ 1 \\ 1 \\ 1 \\ 1 \\ 1i \\ -1i \\ 1 \\ 1 \\ 1i \\ -1i \\ 1i \\ -1i \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.003738 \\ 0.005208 \\ 0.005208 \\ 0.016016 \\ 0.016016 \\ 0.025208 \\ 0.025208 \\ 0.019955 \\ 0.019955 \\ 0.006655 \\ 0.008251 \\ 0.020756 \\ 0.020756 \\ 0.010144 \\ 0.010144 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.011409 \\ 0.013921 \\ 0.013921 \\ 0.020085 \\ 0.020085 \\ 0.02497 \\ 0.02497 \\ 0.006584 \\ 0.006584 \\ 0.042272 \\ 0.038761 \\ 0.038939 \\ 0.038939 \\ 0.01071 \\ 0.01071 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.003738 \\ 0.004337 \\ 0.004337 \\ 0.005119 \\ 0.005119 \\ 0.006075 \\ 0.006075 \\ 0.006022 \\ 0.006022 \\ 0.006655 \\ 0.008251 \\ 0.009422 \\ 0.009422 \\ 0.009877 \\ 0.009877 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.011409 \\ 0.012461 \\ 0.012461 \\ 0.010068 \\ 0.010068 \\ 0.017847 \\ 0.017847 \\ 0.004665 \\ 0.004665 \\ 0.042272 \\ 0.038761 \\ 0.037691 \\ 0.037691 \\ 0.008129 \\ 0.008129 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ -0.003745 \\ -0.004342 \\ -0.004342 \\ -0.005016 \\ -0.005016 \\ -0.005791 \\ -0.005791 \\ -0.005857 \\ -0.005857 \\ -0.006677 \\ -0.008286 \\ -0.009293 \\ -0.009293 \\ -0.009923 \\ -0.009923 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.011387 \\ 0.006256 \\ -0.00621 \\ 0.010477 \\ 0.009955 \\ 0.018352 \\ 0.017518 \\ 0.004761 \\ -0.004581 \\ 0.041674 \\ 0.038339 \\ 0.009831 \\ -0.009901 \\ 0.007071 \\ -0.007015 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0.500922 \\ -0.500922 \\ 0.004855 \\ -0.004855 \\ 0.007834 \\ -0.007834 \\ 0.493908 \\ -0.493908 \\ 0 \\ 0 \\ 0.505942 \\ -0.505942 \\ 0.499257 \\ -0.499257 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ -0.003965 \\ 0.004003 \\ 0.005453 \\ 0.005553 \\ 0.00535 \\ 0.005631 \\ -0.001458 \\ 0.001529 \\ 0 \\ 0 \\ -0.01205 \\ 0.012172 \\ -0.00259 \\ 0.002637 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0.003745 \\ 0.004342 \\ 0.004342 \\ 0.005016 \\ 0.005016 \\ 0.005791 \\ 0.005791 \\ 0.005857 \\ 0.005857 \\ 0.006677 \\ 0.008286 \\ 0.009293 \\ 0.009293 \\ 0.009923 \\ 0.009923 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.011387 \\ 0.006256 \\ 0.00621 \\ 0.010477 \\ 0.009955 \\ 0.018352 \\ 0.017518 \\ 0.004761 \\ 0.004581 \\ 0.041674 \\ 0.038339 \\ 0.009831 \\ 0.009901 \\ 0.007071 \\ 0.007015 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0.000922 \\ 0.000922 \\ 0.004855 \\ 0.004855 \\ 0.007834 \\ 0.007834 \\ 0.006092 \\ 0.006092 \\ 0 \\ 0 \\ 0.005942 \\ 0.005942 \\ 0.000743 \\ 0.000743 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0.003965 \\ 0.004003 \\ 0.005453 \\ 0.005553 \\ 0.00535 \\ 0.005631 \\ 0.001458 \\ 0.001529 \\ 0 \\ 0 \\ 0.01205 \\ 0.012172 \\ 0.00259 \\ 0.002637 \end{pmatrix} $ π
Gypi2:0$ \begin{pmatrix} 1 \\ 0.995519e^{i0.000\pi} \\ 0.995519e^{-i0.000\pi} \\ 0.995479e^{i0.501\pi} \\ 0.995479e^{-i0.501\pi} \\ 0.993242e^{i0.502\pi} \\ 0.993242e^{-i0.502\pi} \\ 0.99117 \\ 0.987858e^{i0.014\pi} \\ 0.987858e^{-i0.014\pi} \\ 0.987177e^{i0.515\pi} \\ 0.987177e^{-i0.515\pi} \\ 0.984056e^{i0.489\pi} \\ 0.984056e^{-i0.489\pi} \\ 0.982904e^{i0.011\pi} \\ 0.982904e^{-i0.011\pi} \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.016552e^{i0.352\pi} \\ 0.016552e^{i0.352\pi} \\ 0.009933e^{i0.202\pi} \\ 0.009933e^{i0.202\pi} \\ 0.016999e^{i0.132\pi} \\ 0.016999e^{i0.132\pi} \\ 0.023078 \\ 0.004973e^{i0.076\pi} \\ 0.004973e^{i0.076\pi} \\ 0.03488e^{i0.248\pi} \\ 0.03488e^{i0.248\pi} \\ 0.030281e^{i0.308\pi} \\ 0.030281e^{i0.308\pi} \\ 0.044571e^{i0.343\pi} \\ 0.044571e^{i0.343\pi} \end{pmatrix} $ $ \begin{pmatrix} 1 \\ 1 \\ 1 \\ 1i \\ -1i \\ 1i \\ -1i \\ 1 \\ 1 \\ 1 \\ 1i \\ -1i \\ 1i \\ -1i \\ 1 \\ 1 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.004505 \\ 0.004505 \\ 0.005523 \\ 0.005523 \\ 0.008997 \\ 0.008997 \\ 0.00883 \\ 0.045408 \\ 0.045408 \\ 0.047332 \\ 0.047332 \\ 0.036861 \\ 0.036861 \\ 0.038701 \\ 0.038701 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.016552 \\ 0.016552 \\ 0.009933 \\ 0.009933 \\ 0.016999 \\ 0.016999 \\ 0.023078 \\ 0.004973 \\ 0.004973 \\ 0.03488 \\ 0.03488 \\ 0.030281 \\ 0.030281 \\ 0.044571 \\ 0.044571 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.004481 \\ 0.004481 \\ 0.004526 \\ 0.004526 \\ 0.006776 \\ 0.006776 \\ 0.00883 \\ 0.0131 \\ 0.0131 \\ 0.013861 \\ 0.013861 \\ 0.016496 \\ 0.016496 \\ 0.017699 \\ 0.017699 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.007431 \\ 0.007431 \\ 0.007995 \\ 0.007995 \\ 0.015552 \\ 0.015552 \\ 0.023078 \\ 0.004834 \\ 0.004834 \\ 0.024824 \\ 0.024824 \\ 0.017204 \\ 0.017204 \\ 0.021099 \\ 0.021099 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ -0.004491 \\ -0.004491 \\ -0.004531 \\ -0.004531 \\ -0.006781 \\ -0.006781 \\ -0.008869 \\ -0.012217 \\ -0.012217 \\ -0.012906 \\ -0.012906 \\ -0.016072 \\ -0.016072 \\ -0.017244 \\ -0.017244 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.007552 \\ 0.007539 \\ 0.005911 \\ -0.005932 \\ 0.006915 \\ -0.006904 \\ 0.023016 \\ 0.004929 \\ 0.004826 \\ 0.023696 \\ -0.025988 \\ 0.025696 \\ -0.024857 \\ 0.023327 \\ 0.020649 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.000148 \\ -0.000148 \\ 0.501012 \\ -0.501012 \\ 0.501897 \\ -0.501897 \\ 0 \\ 0.014014 \\ -0.014014 \\ 0.514598 \\ -0.514598 \\ 0.489335 \\ -0.489335 \\ 0.011148 \\ -0.011148 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0.004693 \\ 0.004695 \\ -0.002547 \\ 0.002566 \\ -0.004963 \\ 0.005005 \\ 0 \\ 0.000307 \\ 0.000443 \\ -0.008163 \\ 0.007836 \\ -0.005158 \\ 0.005979 \\ 0.012183 \\ 0.012685 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0.004491 \\ 0.004491 \\ 0.004531 \\ 0.004531 \\ 0.006781 \\ 0.006781 \\ 0.008869 \\ 0.012217 \\ 0.012217 \\ 0.012906 \\ 0.012906 \\ 0.016072 \\ 0.016072 \\ 0.017244 \\ 0.017244 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.007552 \\ 0.007539 \\ 0.005911 \\ 0.005932 \\ 0.006915 \\ 0.006904 \\ 0.023016 \\ 0.004929 \\ 0.004826 \\ 0.023696 \\ 0.025988 \\ 0.025696 \\ 0.024857 \\ 0.023327 \\ 0.020649 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.000148 \\ 0.000148 \\ 0.001012 \\ 0.001012 \\ 0.001897 \\ 0.001897 \\ 0 \\ 0.014014 \\ 0.014014 \\ 0.014598 \\ 0.014598 \\ 0.010665 \\ 0.010665 \\ 0.011148 \\ 0.011148 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0.004693 \\ 0.004695 \\ 0.002547 \\ 0.002566 \\ 0.004963 \\ 0.005005 \\ 0 \\ 0.000307 \\ 0.000443 \\ 0.008163 \\ 0.007836 \\ 0.005158 \\ 0.005979 \\ 0.012183 \\ 0.012685 \end{pmatrix} $ π
Gcphase:0:1$ \begin{pmatrix} 1 \\ 0.996117 \\ 0.983788e^{i0.009\pi} \\ 0.983788e^{-i0.009\pi} \\ 0.983255e^{i0.983\pi} \\ 0.983255e^{-i0.983\pi} \\ 0.979147e^{i0.001\pi} \\ 0.979147e^{-i0.001\pi} \\ 0.976084e^{i0.016\pi} \\ 0.976084e^{-i0.016\pi} \\ 0.971781e^{i0.007\pi} \\ 0.971781e^{-i0.007\pi} \\ 0.97097e^{i0.993\pi} \\ 0.97097e^{-i0.993\pi} \\ 0.957648e^{i0.976\pi} \\ 0.957648e^{-i0.976\pi} \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.00159 \\ 0.057165e^{i0.337\pi} \\ 0.057165e^{i0.337\pi} \\ 0.016817e^{i0.290\pi} \\ 0.016817e^{i0.290\pi} \\ 0.025934e^{i0.183\pi} \\ 0.025934e^{i0.183\pi} \\ 0.045487e^{i0.269\pi} \\ 0.045487e^{i0.269\pi} \\ 0.073076e^{i0.319\pi} \\ 0.073076e^{i0.319\pi} \\ 0.026551e^{i0.378\pi} \\ 0.026551e^{i0.378\pi} \\ 0.021225e^{i0.085\pi} \\ 0.021225e^{i0.085\pi} \end{pmatrix} $ $ \begin{pmatrix} 1 \\ 1 \\ 1 \\ 1 \\ -1 \\ -1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ -1 \\ -1 \\ -1 \\ -1 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.003883 \\ 0.033357 \\ 0.033357 \\ 0.054973 \\ 0.054973 \\ 0.021034 \\ 0.021034 \\ 0.05589 \\ 0.05589 \\ 0.035539 \\ 0.035539 \\ 0.035696 \\ 0.035696 \\ 0.086282 \\ 0.086282 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.00159 \\ 0.057165 \\ 0.057165 \\ 0.016817 \\ 0.016817 \\ 0.025934 \\ 0.025934 \\ 0.045487 \\ 0.045487 \\ 0.073076 \\ 0.073076 \\ 0.026551 \\ 0.026551 \\ 0.021225 \\ 0.021225 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.003883 \\ 0.016637 \\ 0.016637 \\ 0.018116 \\ 0.018116 \\ 0.020857 \\ 0.020857 \\ 0.025191 \\ 0.025191 \\ 0.028452 \\ 0.028452 \\ 0.029246 \\ 0.029246 \\ 0.045177 \\ 0.045177 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.00159 \\ 0.028062 \\ 0.028062 \\ 0.010301 \\ 0.010301 \\ 0.021772 \\ 0.021772 \\ 0.030165 \\ 0.030165 \\ 0.039399 \\ 0.039399 \\ 0.009896 \\ 0.009896 \\ 0.020473 \\ 0.020473 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ -0.00389 \\ -0.016345 \\ -0.016345 \\ -0.016887 \\ -0.016887 \\ -0.021074 \\ -0.021074 \\ -0.024206 \\ -0.024206 \\ -0.028625 \\ -0.028625 \\ -0.02946 \\ -0.02946 \\ -0.043275 \\ -0.043275 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.001595 \\ 0.030725 \\ 0.027918 \\ -0.009696 \\ -0.011153 \\ 0.02213 \\ 0.022053 \\ 0.032644 \\ 0.029292 \\ 0.042858 \\ 0.040304 \\ -0.009368 \\ -0.010459 \\ -0.021059 \\ -0.021996 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0.009356 \\ -0.009356 \\ 0.98319 \\ -0.98319 \\ 0.000884 \\ -0.000884 \\ 0.016277 \\ -0.016277 \\ 0.006976 \\ -0.006976 \\ 0.99329 \\ -0.99329 \\ 0.975543 \\ -0.975543 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0.015367 \\ 0.01593 \\ -0.004517 \\ -0.004167 \\ 0.004461 \\ 0.0045 \\ 0.010247 \\ 0.011259 \\ 0.019049 \\ 0.019642 \\ -0.008221 \\ 1.991908 \\ -0.002428 \\ -0.001362 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0.00389 \\ 0.016345 \\ 0.016345 \\ 0.016887 \\ 0.016887 \\ 0.021074 \\ 0.021074 \\ 0.024206 \\ 0.024206 \\ 0.028625 \\ 0.028625 \\ 0.02946 \\ 0.02946 \\ 0.043275 \\ 0.043275 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.001595 \\ 0.030725 \\ 0.027918 \\ 0.009696 \\ 0.011153 \\ 0.02213 \\ 0.022053 \\ 0.032644 \\ 0.029292 \\ 0.042858 \\ 0.040304 \\ 0.009368 \\ 0.010459 \\ 0.021059 \\ 0.021996 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0.009356 \\ 0.009356 \\ 0.01681 \\ 1.98319 \\ 0.000884 \\ 0.000884 \\ 0.016277 \\ 0.016277 \\ 0.006976 \\ 0.006976 \\ 0.00671 \\ 1.99329 \\ 0.024457 \\ 1.975543 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0.015367 \\ 0.01593 \\ 0.004517 \\ 0.004167 \\ 0.004461 \\ 0.0045 \\ 0.010247 \\ 0.011259 \\ 0.019049 \\ 0.019642 \\ 0.008221 \\ 1.991908 \\ 0.002428 \\ 0.001362 \end{pmatrix} $ π
Gate Eigenvalues ($E$) Target Evals. ($T$) $|E - T|$ $1.0 - \mathrm{Re}(\bar{T}\cdot E)$ $\mathrm{Re} \log(E)$ $\mathrm{Im} \log(E)$ $|\mathrm{Re}(\log E) - \mathrm{Re}(\log T)|$ $|\mathrm{Im}(\log E) - \mathrm{Im}(\log T)|$
[]$ \begin{pmatrix} 1 \\ 0.998714e^{i0.000\pi} \\ 0.998714e^{-i0.000\pi} \\ 0.993885e^{i0.003\pi} \\ 0.993885e^{-i0.003\pi} \\ 0.993869e^{i0.006\pi} \\ 0.993869e^{-i0.006\pi} \\ 0.992606 \\ 0.991243e^{i0.004\pi} \\ 0.991243e^{-i0.004\pi} \\ 0.988074e^{i0.000\pi} \\ 0.988074e^{-i0.000\pi} \\ 0.985941e^{i0.002\pi} \\ 0.985941e^{-i0.002\pi} \\ 0.985839e^{i0.006\pi} \\ 0.985839e^{-i0.006\pi} \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.02222e^{i0.422\pi} \\ 0.02222e^{i0.422\pi} \\ 0.046623e^{i0.386\pi} \\ 0.046623e^{i0.386\pi} \\ 0.042233e^{i0.370\pi} \\ 0.042233e^{i0.370\pi} \\ 0.099689 \\ 0.070182e^{i0.296\pi} \\ 0.070182e^{i0.296\pi} \\ 0.05523e^{i0.308\pi} \\ 0.05523e^{i0.308\pi} \\ 0.06728e^{i0.202\pi} \\ 0.06728e^{i0.202\pi} \\ 0.046658e^{i0.368\pi} \\ 0.046658e^{i0.368\pi} \end{pmatrix} $ $ \begin{pmatrix} 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.001292 \\ 0.001292 \\ 0.01045 \\ 0.01045 \\ 0.019453 \\ 0.019453 \\ 0.007394 \\ 0.014434 \\ 0.014434 \\ 0.011967 \\ 0.011967 \\ 0.015754 \\ 0.015754 \\ 0.023963 \\ 0.023963 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.02222 \\ 0.02222 \\ 0.046623 \\ 0.046623 \\ 0.042233 \\ 0.042233 \\ 0.099689 \\ 0.070182 \\ 0.070182 \\ 0.05523 \\ 0.05523 \\ 0.06728 \\ 0.06728 \\ 0.046658 \\ 0.046658 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.001286 \\ 0.001286 \\ 0.006151 \\ 0.006151 \\ 0.006301 \\ 0.006301 \\ 0.007394 \\ 0.008823 \\ 0.008823 \\ 0.011927 \\ 0.011927 \\ 0.014084 \\ 0.014084 \\ 0.014348 \\ 0.014348 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.005405 \\ 0.005405 \\ 0.016356 \\ 0.016356 \\ 0.016764 \\ 0.016764 \\ 0.099689 \\ 0.04192 \\ 0.04192 \\ 0.031377 \\ 0.031377 \\ 0.054243 \\ 0.054243 \\ 0.018749 \\ 0.018749 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ -0.001287 \\ -0.001287 \\ -0.006134 \\ -0.006134 \\ -0.00615 \\ -0.00615 \\ -0.007422 \\ -0.008796 \\ -0.008796 \\ -0.011998 \\ -0.011998 \\ -0.014159 \\ -0.014159 \\ -0.014262 \\ -0.014262 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.00563 \\ 0.005625 \\ 0.017615 \\ 0.016894 \\ 0.018156 \\ 0.016762 \\ 0.095703 \\ 0.0435 \\ 0.042299 \\ 0.032297 \\ 0.032212 \\ 0.054546 \\ 0.054027 \\ 0.02055 \\ 0.018928 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.000039 \\ -0.000039 \\ 0.002706 \\ -0.002706 \\ 0.005895 \\ -0.005895 \\ 0 \\ 0.003668 \\ -0.003668 \\ 0.000315 \\ -0.000315 \\ 0.002279 \\ -0.002279 \\ 0.006197 \\ -0.006197 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0.006831 \\ 0.006831 \\ 0.013699 \\ 0.013796 \\ 0.012095 \\ 0.012307 \\ 0 \\ 0.017164 \\ 0.017483 \\ 0.014172 \\ 0.014193 \\ 0.012052 \\ 0.012296 \\ 0.013401 \\ 0.013654 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0.001287 \\ 0.001287 \\ 0.006134 \\ 0.006134 \\ 0.00615 \\ 0.00615 \\ 0.007422 \\ 0.008796 \\ 0.008796 \\ 0.011998 \\ 0.011998 \\ 0.014159 \\ 0.014159 \\ 0.014262 \\ 0.014262 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.00563 \\ 0.005625 \\ 0.017615 \\ 0.016894 \\ 0.018156 \\ 0.016762 \\ 0.095703 \\ 0.0435 \\ 0.042299 \\ 0.032297 \\ 0.032212 \\ 0.054546 \\ 0.054027 \\ 0.02055 \\ 0.018928 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.000039 \\ 0.000039 \\ 0.002706 \\ 0.002706 \\ 0.005895 \\ 0.005895 \\ 0 \\ 0.003668 \\ 0.003668 \\ 0.000315 \\ 0.000315 \\ 0.002279 \\ 0.002279 \\ 0.006197 \\ 0.006197 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0.006831 \\ 0.006831 \\ 0.013699 \\ 0.013796 \\ 0.012095 \\ 0.012307 \\ 0 \\ 0.017164 \\ 0.017483 \\ 0.014172 \\ 0.014193 \\ 0.012052 \\ 0.012296 \\ 0.013401 \\ 0.013654 \end{pmatrix} $ π
Gxpi2:1$ \begin{pmatrix} 1 \\ 0.9987 \\ 0.996318e^{i0.500\pi} \\ 0.996318e^{-i0.500\pi} \\ 0.996204e^{i0.500\pi} \\ 0.996204e^{-i0.500\pi} \\ 0.995062 \\ 0.992519 \\ 0.988418 \\ 0.985917 \\ 0.985001e^{i0.500\pi} \\ 0.985001e^{-i0.500\pi} \\ 0.984622e^{i0.500\pi} \\ 0.984622e^{-i0.500\pi} \\ 0.982011e^{i0.000\pi} \\ 0.982011e^{-i0.000\pi} \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.003619 \\ 0.009203e^{i0.125\pi} \\ 0.009203e^{i0.125\pi} \\ 0.01311e^{i0.170\pi} \\ 0.01311e^{i0.170\pi} \\ 0.005307 \\ 0.077538 \\ 0.094314 \\ 0.043156 \\ 0.031025e^{i0.364\pi} \\ 0.031025e^{i0.364\pi} \\ 0.044919e^{i0.256\pi} \\ 0.044919e^{i0.256\pi} \\ 0.02034e^{i0.335\pi} \\ 0.02034e^{i0.335\pi} \end{pmatrix} $ $ \begin{pmatrix} 1 \\ 1 \\ 1i \\ -1i \\ 1i \\ -1i \\ 1 \\ 1 \\ 1 \\ 1 \\ 1i \\ -1i \\ 1i \\ -1i \\ 1 \\ 1 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.0013 \\ 0.003727 \\ 0.003727 \\ 0.003884 \\ 0.003884 \\ 0.004938 \\ 0.007481 \\ 0.011582 \\ 0.014083 \\ 0.015019 \\ 0.015019 \\ 0.015412 \\ 0.015412 \\ 0.018019 \\ 0.018019 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.003619 \\ 0.009203 \\ 0.009203 \\ 0.01311 \\ 0.01311 \\ 0.005307 \\ 0.077538 \\ 0.094314 \\ 0.043156 \\ 0.031025 \\ 0.031025 \\ 0.044919 \\ 0.044919 \\ 0.02034 \\ 0.02034 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.0013 \\ 0.003682 \\ 0.003682 \\ 0.003796 \\ 0.003796 \\ 0.004938 \\ 0.007481 \\ 0.011582 \\ 0.014083 \\ 0.014999 \\ 0.014999 \\ 0.015378 \\ 0.015378 \\ 0.01799 \\ 0.01799 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.003619 \\ 0.008497 \\ 0.008497 \\ 0.011286 \\ 0.011286 \\ 0.005307 \\ 0.077538 \\ 0.094314 \\ 0.043156 \\ 0.012828 \\ 0.012828 \\ 0.031168 \\ 0.031168 \\ 0.010067 \\ 0.010067 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ -0.001301 \\ -0.003689 \\ -0.003689 \\ -0.003803 \\ -0.003803 \\ -0.00495 \\ -0.007509 \\ -0.011649 \\ -0.014183 \\ -0.015112 \\ -0.015112 \\ -0.015497 \\ -0.015497 \\ -0.018153 \\ -0.018153 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.003617 \\ 0.003572 \\ -0.003522 \\ 0.006745 \\ -0.006643 \\ 0.005319 \\ 0.075221 \\ 0.091137 \\ 0.042842 \\ 0.028346 \\ -0.029019 \\ 0.032824 \\ -0.032834 \\ 0.010376 \\ 0.010339 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0.500184 \\ -0.500184 \\ 0.499738 \\ -0.499738 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0.500251 \\ -0.500251 \\ 0.499672 \\ -0.499672 \\ 0.000331 \\ -0.000331 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ -0.002706 \\ 0.002724 \\ -0.00358 \\ 0.003632 \\ 0 \\ 0 \\ 0 \\ 0 \\ -0.004037 \\ 0.00426 \\ -0.009742 \\ 0.010425 \\ 0.005667 \\ 0.005674 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0.001301 \\ 0.003689 \\ 0.003689 \\ 0.003803 \\ 0.003803 \\ 0.00495 \\ 0.007509 \\ 0.011649 \\ 0.014183 \\ 0.015112 \\ 0.015112 \\ 0.015497 \\ 0.015497 \\ 0.018153 \\ 0.018153 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.003617 \\ 0.003572 \\ 0.003522 \\ 0.006745 \\ 0.006643 \\ 0.005319 \\ 0.075221 \\ 0.091137 \\ 0.042842 \\ 0.028346 \\ 0.029019 \\ 0.032824 \\ 0.032834 \\ 0.010376 \\ 0.010339 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0.000184 \\ 0.000184 \\ 0.000262 \\ 0.000262 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0.000251 \\ 0.000251 \\ 0.000328 \\ 0.000328 \\ 0.000331 \\ 0.000331 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0.002706 \\ 0.002724 \\ 0.00358 \\ 0.003632 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0.004037 \\ 0.00426 \\ 0.009742 \\ 0.010425 \\ 0.005667 \\ 0.005674 \end{pmatrix} $ π
Gxpi2:0$ \begin{pmatrix} 1 \\ 0.997864 \\ 0.993764e^{i0.505\pi} \\ 0.993764e^{-i0.505\pi} \\ 0.993697e^{i0.511\pi} \\ 0.993697e^{-i0.511\pi} \\ 0.989939e^{i0.518\pi} \\ 0.989939e^{-i0.518\pi} \\ 0.989934e^{i0.499\pi} \\ 0.989934e^{-i0.499\pi} \\ 0.989915e^{i0.012\pi} \\ 0.989915e^{-i0.012\pi} \\ 0.989722 \\ 0.989652e^{i0.007\pi} \\ 0.989652e^{-i0.007\pi} \\ 0.988364 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.00878 \\ 0.008449e^{i0.334\pi} \\ 0.008449e^{i0.334\pi} \\ 0.012314e^{i0.259\pi} \\ 0.012314e^{i0.259\pi} \\ 0.034277e^{i0.312\pi} \\ 0.034277e^{i0.312\pi} \\ 0.024184e^{i0.192\pi} \\ 0.024184e^{i0.192\pi} \\ 0.034863e^{i0.265\pi} \\ 0.034863e^{i0.265\pi} \\ 0.009148 \\ 0.055108e^{i0.418\pi} \\ 0.055108e^{i0.418\pi} \\ 0.013582 \end{pmatrix} $ $ \begin{pmatrix} 1 \\ 1 \\ 1i \\ -1i \\ 1i \\ -1i \\ 1i \\ -1i \\ 1i \\ -1i \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.002136 \\ 0.017216 \\ 0.017216 \\ 0.035663 \\ 0.035663 \\ 0.056046 \\ 0.056046 \\ 0.010865 \\ 0.010865 \\ 0.03961 \\ 0.03961 \\ 0.010278 \\ 0.023267 \\ 0.023267 \\ 0.011636 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.00878 \\ 0.008449 \\ 0.008449 \\ 0.012314 \\ 0.012314 \\ 0.034277 \\ 0.034277 \\ 0.024184 \\ 0.024184 \\ 0.034863 \\ 0.034863 \\ 0.009148 \\ 0.055108 \\ 0.055108 \\ 0.013582 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.002136 \\ 0.006364 \\ 0.006364 \\ 0.006919 \\ 0.006919 \\ 0.011581 \\ 0.011581 \\ 0.010074 \\ 0.010074 \\ 0.010819 \\ 0.010819 \\ 0.010278 \\ 0.010565 \\ 0.010565 \\ 0.011636 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.00878 \\ 0.004209 \\ 0.004209 \\ 0.008451 \\ 0.008451 \\ 0.019081 \\ 0.019081 \\ 0.019931 \\ 0.019931 \\ 0.023446 \\ 0.023446 \\ 0.009148 \\ 0.01411 \\ 0.01411 \\ 0.013582 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ -0.002138 \\ -0.006255 \\ -0.006255 \\ -0.006322 \\ -0.006322 \\ -0.010112 \\ -0.010112 \\ -0.010117 \\ -0.010117 \\ -0.010136 \\ -0.010136 \\ -0.010331 \\ -0.010402 \\ -0.010402 \\ -0.011705 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.00876 \\ 0.007285 \\ -0.007458 \\ 0.008709 \\ -0.009316 \\ 0.027483 \\ -0.030075 \\ 0.01402 \\ -0.01364 \\ 0.024672 \\ 0.022759 \\ 0.009201 \\ 0.016652 \\ 0.014466 \\ 0.013648 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0.505124 \\ -0.505124 \\ 0.511209 \\ -0.511209 \\ 0.517641 \\ -0.517641 \\ 0.498692 \\ -0.498692 \\ 0.012255 \\ -0.012255 \\ 0 \\ 0.006668 \\ -0.006668 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ -0.001376 \\ 0.00132 \\ -0.002782 \\ 0.002629 \\ -0.006454 \\ 0.005791 \\ -0.006302 \\ 0.006516 \\ 0.007806 \\ 0.008388 \\ 0 \\ 0.016761 \\ 0.016986 \\ 0 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0.002138 \\ 0.006255 \\ 0.006255 \\ 0.006322 \\ 0.006322 \\ 0.010112 \\ 0.010112 \\ 0.010117 \\ 0.010117 \\ 0.010136 \\ 0.010136 \\ 0.010331 \\ 0.010402 \\ 0.010402 \\ 0.011705 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.00876 \\ 0.007285 \\ 0.007458 \\ 0.008709 \\ 0.009316 \\ 0.027483 \\ 0.030075 \\ 0.01402 \\ 0.01364 \\ 0.024672 \\ 0.022759 \\ 0.009201 \\ 0.016652 \\ 0.014466 \\ 0.013648 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0.005124 \\ 0.005124 \\ 0.011209 \\ 0.011209 \\ 0.017641 \\ 0.017641 \\ 0.001308 \\ 0.001308 \\ 0.012255 \\ 0.012255 \\ 0 \\ 0.006668 \\ 0.006668 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0.001376 \\ 0.00132 \\ 0.002782 \\ 0.002629 \\ 0.006454 \\ 0.005791 \\ 0.006302 \\ 0.006516 \\ 0.007806 \\ 0.008388 \\ 0 \\ 0.016761 \\ 0.016986 \\ 0 \end{pmatrix} $ π
Gypi2:1$ \begin{pmatrix} 1 \\ 0.997035 \\ 0.99454e^{i0.502\pi} \\ 0.99454e^{-i0.502\pi} \\ 0.990289e^{i0.009\pi} \\ 0.990289e^{-i0.009\pi} \\ 0.989971e^{i0.012\pi} \\ 0.989971e^{-i0.012\pi} \\ 0.988971e^{i0.512\pi} \\ 0.988971e^{-i0.512\pi} \\ 0.988921e^{i0.491\pi} \\ 0.988921e^{-i0.491\pi} \\ 0.985644 \\ 0.984269e^{i0.502\pi} \\ 0.984269e^{-i0.502\pi} \\ 0.98339 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.010709 \\ 0.016056e^{i0.308\pi} \\ 0.016056e^{i0.308\pi} \\ 0.030592e^{i0.157\pi} \\ 0.030592e^{i0.157\pi} \\ 0.034405e^{i0.146\pi} \\ 0.034405e^{i0.146\pi} \\ 0.062388e^{i0.187\pi} \\ 0.062388e^{i0.187\pi} \\ 0.040223e^{i0.084\pi} \\ 0.040223e^{i0.084\pi} \\ 0.014925 \\ 0.121571e^{i0.056\pi} \\ 0.121571e^{i0.056\pi} \\ 0.063247 \end{pmatrix} $ $ \begin{pmatrix} 1 \\ 1 \\ 1i \\ -1i \\ 1 \\ 1 \\ 1 \\ 1 \\ 1i \\ -1i \\ 1i \\ -1i \\ 1 \\ 1i \\ -1i \\ 1 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.002965 \\ 0.007242 \\ 0.007242 \\ 0.030046 \\ 0.030046 \\ 0.038711 \\ 0.038711 \\ 0.039205 \\ 0.039205 \\ 0.030259 \\ 0.030259 \\ 0.014356 \\ 0.016418 \\ 0.016418 \\ 0.01661 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.010709 \\ 0.016056 \\ 0.016056 \\ 0.030592 \\ 0.030592 \\ 0.034405 \\ 0.034405 \\ 0.062388 \\ 0.062388 \\ 0.040223 \\ 0.040223 \\ 0.014925 \\ 0.121571 \\ 0.121571 \\ 0.063247 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.002965 \\ 0.005471 \\ 0.005471 \\ 0.010116 \\ 0.010116 \\ 0.010728 \\ 0.010728 \\ 0.011736 \\ 0.011736 \\ 0.011475 \\ 0.011475 \\ 0.014356 \\ 0.015742 \\ 0.015742 \\ 0.01661 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.010709 \\ 0.009126 \\ 0.009126 \\ 0.026929 \\ 0.026929 \\ 0.030827 \\ 0.030827 \\ 0.051969 \\ 0.051969 \\ 0.038834 \\ 0.038834 \\ 0.014925 \\ 0.119683 \\ 0.119683 \\ 0.063247 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ -0.002969 \\ -0.005475 \\ -0.005475 \\ -0.009759 \\ -0.009759 \\ -0.01008 \\ -0.01008 \\ -0.01109 \\ -0.01109 \\ -0.011141 \\ -0.011141 \\ -0.01446 \\ -0.015856 \\ -0.015856 \\ -0.01675 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.010684 \\ 0.013193 \\ -0.013373 \\ 0.027318 \\ 0.026525 \\ 0.0313 \\ 0.03021 \\ 0.033717 \\ -0.036151 \\ 0.012379 \\ -0.008731 \\ 0.015028 \\ 0.02794 \\ -0.01485 \\ 0.062332 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0.501519 \\ -0.501519 \\ 0.009095 \\ -0.009095 \\ 0.011962 \\ -0.011962 \\ 0.512043 \\ -0.512043 \\ 0.490987 \\ -0.490987 \\ 0 \\ 0.501508 \\ -0.501508 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ -0.002903 \\ 0.00294 \\ 0.004297 \\ 0.004783 \\ 0.004397 \\ 0.005125 \\ -0.016574 \\ 0.016902 \\ -0.01225 \\ 0.012704 \\ 0 \\ -0.037759 \\ 0.039351 \\ 0 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0.002969 \\ 0.005475 \\ 0.005475 \\ 0.009759 \\ 0.009759 \\ 0.01008 \\ 0.01008 \\ 0.01109 \\ 0.01109 \\ 0.011141 \\ 0.011141 \\ 0.01446 \\ 0.015856 \\ 0.015856 \\ 0.01675 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.010684 \\ 0.013193 \\ 0.013373 \\ 0.027318 \\ 0.026525 \\ 0.0313 \\ 0.03021 \\ 0.033717 \\ 0.036151 \\ 0.012379 \\ 0.008731 \\ 0.015028 \\ 0.02794 \\ 0.01485 \\ 0.062332 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0.001519 \\ 0.001519 \\ 0.009095 \\ 0.009095 \\ 0.011962 \\ 0.011962 \\ 0.012043 \\ 0.012043 \\ 0.009013 \\ 0.009013 \\ 0 \\ 0.001508 \\ 0.001508 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0.002903 \\ 0.00294 \\ 0.004297 \\ 0.004783 \\ 0.004397 \\ 0.005125 \\ 0.016574 \\ 0.016902 \\ 0.01225 \\ 0.012704 \\ 0 \\ 0.037759 \\ 0.039351 \\ 0 \end{pmatrix} $ π
Gypi2:0$ \begin{pmatrix} 1 \\ 0.999002 \\ 0.996094e^{i0.503\pi} \\ 0.996094e^{-i0.503\pi} \\ 0.996014e^{i0.507\pi} \\ 0.996014e^{-i0.507\pi} \\ 0.992873 \\ 0.992701 \\ 0.983344e^{i0.518\pi} \\ 0.983344e^{-i0.518\pi} \\ 0.983296e^{i0.015\pi} \\ 0.983296e^{-i0.015\pi} \\ 0.983063e^{i0.011\pi} \\ 0.983063e^{-i0.011\pi} \\ 0.983052e^{i0.492\pi} \\ 0.983052e^{-i0.492\pi} \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.003308 \\ 0.009424e^{i0.187\pi} \\ 0.009424e^{i0.187\pi} \\ 0.021644e^{i0.074\pi} \\ 0.021644e^{i0.074\pi} \\ 0.02175 \\ 0.034408 \\ 0.059387e^{i0.446\pi} \\ 0.059387e^{i0.446\pi} \\ 0.074565e^{i0.208\pi} \\ 0.074565e^{i0.208\pi} \\ 0.041644e^{i0.259\pi} \\ 0.041644e^{i0.259\pi} \\ 0.042314e^{i0.321\pi} \\ 0.042314e^{i0.321\pi} \end{pmatrix} $ $ \begin{pmatrix} 1 \\ 1 \\ 1i \\ -1i \\ 1i \\ -1i \\ 1 \\ 1 \\ 1i \\ -1i \\ 1 \\ 1 \\ 1 \\ 1 \\ 1i \\ -1i \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.000998 \\ 0.009903 \\ 0.009903 \\ 0.022719 \\ 0.022719 \\ 0.007127 \\ 0.007299 \\ 0.058024 \\ 0.058024 \\ 0.048601 \\ 0.048601 \\ 0.03821 \\ 0.03821 \\ 0.029641 \\ 0.029641 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.003308 \\ 0.009424 \\ 0.009424 \\ 0.021644 \\ 0.021644 \\ 0.02175 \\ 0.034408 \\ 0.059387 \\ 0.059387 \\ 0.074565 \\ 0.074565 \\ 0.041644 \\ 0.041644 \\ 0.042314 \\ 0.042314 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.000998 \\ 0.003948 \\ 0.003948 \\ 0.004236 \\ 0.004236 \\ 0.007127 \\ 0.007299 \\ 0.018201 \\ 0.018201 \\ 0.017745 \\ 0.017745 \\ 0.017523 \\ 0.017523 \\ 0.017243 \\ 0.017243 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.003308 \\ 0.007847 \\ 0.007847 \\ 0.021059 \\ 0.021059 \\ 0.02175 \\ 0.034408 \\ 0.009971 \\ 0.009971 \\ 0.059271 \\ 0.059271 \\ 0.028645 \\ 0.028645 \\ 0.022563 \\ 0.022563 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ -0.000998 \\ -0.003914 \\ -0.003914 \\ -0.003994 \\ -0.003994 \\ -0.007153 \\ -0.007326 \\ -0.016796 \\ -0.016796 \\ -0.016845 \\ -0.016845 \\ -0.017082 \\ -0.017082 \\ -0.017093 \\ -0.017093 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.003305 \\ 0.005184 \\ -0.005293 \\ 0.004755 \\ -0.005281 \\ 0.021669 \\ 0.034073 \\ 0.057286 \\ -0.06186 \\ 0.061291 \\ 0.057531 \\ 0.030153 \\ 0.028149 \\ 0.036524 \\ -0.036192 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0.502902 \\ -0.502902 \\ 0.507134 \\ -0.507134 \\ 0 \\ 0 \\ 0.517844 \\ -0.517844 \\ 0.014652 \\ -0.014652 \\ 0.010997 \\ -0.010997 \\ 0.492193 \\ -0.492193 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ -0.00251 \\ 0.002506 \\ -0.006733 \\ 0.006729 \\ 0 \\ 0 \\ -0.004046 \\ 0.002299 \\ 0.012934 \\ 0.014651 \\ 0.009182 \\ 0.009823 \\ -0.006768 \\ 0.007868 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0.000998 \\ 0.003914 \\ 0.003914 \\ 0.003994 \\ 0.003994 \\ 0.007153 \\ 0.007326 \\ 0.016796 \\ 0.016796 \\ 0.016845 \\ 0.016845 \\ 0.017082 \\ 0.017082 \\ 0.017093 \\ 0.017093 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.003305 \\ 0.005184 \\ 0.005293 \\ 0.004755 \\ 0.005281 \\ 0.021669 \\ 0.034073 \\ 0.057286 \\ 0.06186 \\ 0.061291 \\ 0.057531 \\ 0.030153 \\ 0.028149 \\ 0.036524 \\ 0.036192 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0.002902 \\ 0.002902 \\ 0.007134 \\ 0.007134 \\ 0 \\ 0 \\ 0.017844 \\ 0.017844 \\ 0.014652 \\ 0.014652 \\ 0.010997 \\ 0.010997 \\ 0.007807 \\ 0.007807 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0.00251 \\ 0.002506 \\ 0.006733 \\ 0.006729 \\ 0 \\ 0 \\ 0.004046 \\ 0.002299 \\ 0.012934 \\ 0.014651 \\ 0.009182 \\ 0.009823 \\ 0.006768 \\ 0.007868 \end{pmatrix} $ π
Gcphase:0:1$ \begin{pmatrix} 1 \\ 0.998557 \\ 0.995251 \\ 0.993616 \\ 0.982655e^{i0.017\pi} \\ 0.982655e^{-i0.017\pi} \\ 0.982559e^{i0.009\pi} \\ 0.982559e^{-i0.009\pi} \\ 0.982034e^{i0.982\pi} \\ 0.982034e^{-i0.982\pi} \\ 0.981637e^{i0.974\pi} \\ 0.981637e^{-i0.974\pi} \\ 0.968119e^{i0.007\pi} \\ 0.968119e^{-i0.007\pi} \\ 0.967627e^{i0.991\pi} \\ 0.967627e^{-i0.991\pi} \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.00506 \\ 0.024844 \\ 0.012188 \\ 0.05446e^{i0.154\pi} \\ 0.05446e^{i0.154\pi} \\ 0.029927e^{i0.115\pi} \\ 0.029927e^{i0.115\pi} \\ 0.026108e^{i0.316\pi} \\ 0.026108e^{i0.316\pi} \\ 0.060803e^{i0.249\pi} \\ 0.060803e^{i0.249\pi} \\ 0.045035e^{i0.412\pi} \\ 0.045035e^{i0.412\pi} \\ 0.096531e^{i0.422\pi} \\ 0.096531e^{i0.422\pi} \end{pmatrix} $ $ \begin{pmatrix} 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ -1 \\ -1 \\ -1 \\ -1 \\ 1 \\ 1 \\ -1 \\ -1 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.001443 \\ 0.004749 \\ 0.006384 \\ 0.055819 \\ 0.055819 \\ 0.034317 \\ 0.034317 \\ 0.060234 \\ 0.060234 \\ 0.083001 \\ 0.083001 \\ 0.039018 \\ 0.039018 \\ 0.042665 \\ 0.042665 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.00506 \\ 0.024844 \\ 0.012188 \\ 0.05446 \\ 0.05446 \\ 0.029927 \\ 0.029927 \\ 0.026108 \\ 0.026108 \\ 0.060803 \\ 0.060803 \\ 0.045035 \\ 0.045035 \\ 0.096531 \\ 0.096531 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.001443 \\ 0.004749 \\ 0.006384 \\ 0.018752 \\ 0.018752 \\ 0.017878 \\ 0.017878 \\ 0.019618 \\ 0.019618 \\ 0.021639 \\ 0.021639 \\ 0.032134 \\ 0.032134 \\ 0.032759 \\ 0.032759 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.00506 \\ 0.024844 \\ 0.012188 \\ 0.048212 \\ 0.048212 \\ 0.027979 \\ 0.027979 \\ 0.014237 \\ 0.014237 \\ 0.043157 \\ 0.043157 \\ 0.012358 \\ 0.012358 \\ 0.023429 \\ 0.023429 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ -0.001445 \\ -0.00476 \\ -0.006405 \\ -0.017497 \\ -0.017497 \\ -0.017595 \\ -0.017595 \\ -0.018129 \\ -0.018129 \\ -0.018533 \\ -0.018533 \\ -0.0324 \\ -0.0324 \\ -0.032908 \\ -0.032908 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.005055 \\ 0.024656 \\ 0.012192 \\ 0.049386 \\ 0.046881 \\ 0.028426 \\ 0.027817 \\ -0.012995 \\ -0.015655 \\ -0.039888 \\ -0.047663 \\ 0.014649 \\ 0.012659 \\ -0.016771 \\ -0.022458 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0.017039 \\ -0.017039 \\ 0.009491 \\ -0.009491 \\ 0.98153 \\ -0.98153 \\ 0.973987 \\ -0.973987 \\ 0.007277 \\ -0.007277 \\ 0.991007 \\ -0.991007 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0.007003 \\ 0.008616 \\ 0.00308 \\ 0.003607 \\ -0.007446 \\ -0.006922 \\ -0.0156 \\ -0.013324 \\ 0.013941 \\ 0.014152 \\ -0.031587 \\ 1.96868 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0.001445 \\ 0.00476 \\ 0.006405 \\ 0.017497 \\ 0.017497 \\ 0.017595 \\ 0.017595 \\ 0.018129 \\ 0.018129 \\ 0.018533 \\ 0.018533 \\ 0.0324 \\ 0.0324 \\ 0.032908 \\ 0.032908 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.005055 \\ 0.024656 \\ 0.012192 \\ 0.049386 \\ 0.046881 \\ 0.028426 \\ 0.027817 \\ 0.012995 \\ 0.015655 \\ 0.039888 \\ 0.047663 \\ 0.014649 \\ 0.012659 \\ 0.016771 \\ 0.022458 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0.017039 \\ 0.017039 \\ 0.009491 \\ 0.009491 \\ 0.01847 \\ 1.98153 \\ 0.026013 \\ 1.973987 \\ 0.007277 \\ 0.007277 \\ 0.008993 \\ 1.991007 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0.007003 \\ 0.008616 \\ 0.00308 \\ 0.003607 \\ 0.007446 \\ 0.006922 \\ 0.0156 \\ 0.013324 \\ 0.013941 \\ 0.014152 \\ 0.031587 \\ 1.96868 \end{pmatrix} $ π
Gate Eigenvalues ($E$) Target Evals. ($T$) $|E - T|$ $1.0 - \mathrm{Re}(\bar{T}\cdot E)$ $\mathrm{Re} \log(E)$ $\mathrm{Im} \log(E)$ $|\mathrm{Re}(\log E) - \mathrm{Re}(\log T)|$ $|\mathrm{Im}(\log E) - \mathrm{Im}(\log T)|$
[]$ \begin{pmatrix} 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \end{pmatrix} $ $ \begin{pmatrix} 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π
Gxpi2:1$ \begin{pmatrix} 1i \\ -1i \\ 1i \\ -1i \\ 1 \\ 1i \\ -1i \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1i \\ -1i \\ 1 \end{pmatrix} $ $ \begin{pmatrix} 1i \\ -1i \\ 1i \\ -1i \\ 1 \\ 1i \\ -1i \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1i \\ -1i \\ 1 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0.5 \\ -0.5 \\ 0.5 \\ -0.5 \\ 0 \\ 0.5 \\ -0.5 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0.5 \\ -0.5 \\ 0 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π
Gxpi2:0$ \begin{pmatrix} 1i \\ -1i \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1i \\ -1i \\ 1i \\ -1i \\ 1 \\ 1 \\ 1i \\ -1i \end{pmatrix} $ $ \begin{pmatrix} 1i \\ -1i \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1i \\ -1i \\ 1i \\ -1i \\ 1 \\ 1 \\ 1i \\ -1i \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0.5 \\ -0.5 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0.5 \\ -0.5 \\ 0.5 \\ -0.5 \\ 0 \\ 0 \\ 0.5 \\ -0.5 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π
Gypi2:1$ \begin{pmatrix} 1i \\ -1i \\ 1 \\ 1i \\ -1i \\ 1 \\ 1 \\ 1i \\ -1i \\ 1 \\ 1 \\ 1 \\ 1 \\ 1i \\ -1i \\ 1 \end{pmatrix} $ $ \begin{pmatrix} 1i \\ -1i \\ 1 \\ 1i \\ -1i \\ 1 \\ 1 \\ 1i \\ -1i \\ 1 \\ 1 \\ 1 \\ 1 \\ 1i \\ -1i \\ 1 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0.5 \\ -0.5 \\ 0 \\ 0.5 \\ -0.5 \\ 0 \\ 0 \\ 0.5 \\ -0.5 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0.5 \\ -0.5 \\ 0 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π
Gypi2:0$ \begin{pmatrix} 1i \\ -1i \\ 1i \\ -1i \\ 1 \\ 1i \\ -1i \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1i \\ -1i \\ 1 \end{pmatrix} $ $ \begin{pmatrix} 1i \\ -1i \\ 1i \\ -1i \\ 1 \\ 1i \\ -1i \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1i \\ -1i \\ 1 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0.5 \\ -0.5 \\ 0.5 \\ -0.5 \\ 0 \\ 0.5 \\ -0.5 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0.5 \\ -0.5 \\ 0 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π
Gcphase:0:1$ \begin{pmatrix} 1 \\ -1 \\ 1 \\ 1 \\ 1 \\ -1 \\ 1 \\ 1 \\ -1 \\ 1 \\ 1 \\ 1 \\ 1 \\ -1 \\ -1 \\ -1 \end{pmatrix} $ $ \begin{pmatrix} 1 \\ -1 \\ 1 \\ 1 \\ 1 \\ -1 \\ 1 \\ 1 \\ -1 \\ 1 \\ 1 \\ 1 \\ 1 \\ -1 \\ -1 \\ -1 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 1 \\ 0 \\ 0 \\ 0 \\ 1 \\ 0 \\ 0 \\ 1 \\ 0 \\ 0 \\ 0 \\ 0 \\ 1 \\ 1 \\ 1 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π
Gauge-robust gate set. This table gives a first-order gauge-invariant description of a gate set by decomposing each gate G as G = F^{-1} M G_0 F where M commutes with G_0 and F = exp(r) where r is zero on the diagonal blocks corresponding to the degenerate eigenvalues of G_0.
Gate M - I FinvF([]) - I FinvF(Gxpi2:1) - I FinvF(Gxpi2:0) - I FinvF(Gypi2:1) - I FinvF(Gypi2:0) - I FinvF(Gcphase:0:1) - I
[]
0
Gxpi2:1
0
Gxpi2:0
0
Gypi2:1
0
Gypi2:0
0
Gcphase:0:1
0
Gate M - I FinvF([]) - I FinvF(Gxpi2:1) - I FinvF(Gxpi2:0) - I FinvF(Gypi2:1) - I FinvF(Gypi2:0) - I FinvF(Gcphase:0:1) - I
[]
0
Gxpi2:1
0
Gxpi2:0
0
Gypi2:1
0
Gypi2:0
0
Gcphase:0:1
0
Gate M - I FinvF([]) - I FinvF(Gxpi2:1) - I FinvF(Gxpi2:0) - I FinvF(Gypi2:1) - I FinvF(Gypi2:0) - I FinvF(Gcphase:0:1) - I
[]
0
Gxpi2:1
0
Gxpi2:0
0
Gypi2:1
0
Gypi2:0
0
Gcphase:0:1
0

Gauge Invariant Error Metrics applied to germ sequences

All of the per-gate gauge-invariant metrics of the previous tab are functions of each gate's spectrum and do not account for how the gate relates to other gates. In an attempt to extract some of that information in a gauge-invariant way, this tab looks at the spectra of the germ-sequences. Each germ amplifies (i.e. has eigenvalues which correspond to) certain directions in gate-set space. Some of these directions describe how the single gates relate to one another, and, if an amplificationally complete set of germs was used, every direction is amplified by at least one germ. This implies that the (gauge-invariant) spectra of the germs should constitute a full description of the gate set. This tab compares each germ-spectrum to the spectrum of that germ if it were generated using the set eigenspace-projected gates obtained by placing each gate's GST-estimated eigenvalues within eigenbasis of the ideal target gate.

Discrepancy between germs and spectral gates This table requires some explaining. It tries to answer the following question: "Is it plausible that each gate has only spectral errors, so that its eigenvectors are exactly correct?". GST can more or less directly estimate each gate's spectrum, because that's gauge-invariant. But gate eigenbases are relational to other gates and gauge-variant. To infer them, GST basically does precise spectrum estimation on germs that incorporate multiple gates. Each germ's estimated spectrum is shown elsewhere. This table compares each germ's estimated spectrum to the spectrum it would have if each individual gate had the eigenvalues that GST estimated for it, but exactly the right (target) eigenbasis. This is the "eigenspace-projected" estimate of that gate. Comparing the estimated germ spectra with those predicted by the eigenspace-projected gates yields gauge-invariant metrics of how much of the overall error can be attributed to purely spectral errors in each gate. If the estimated-gate eigenvalues account for everything, all of the discrepancy values in this table would equal zero.
Gate or Germ Eigenvalue 1/2 Diamond-Dist Eigenvalue Non-U. 1/2 Diamond-Dist
[]00
Gxpi2:100
Gxpi2:000
Gypi2:100
Gypi2:000
Gcphase:0:100
Qubit 0 ---|Gxpi2|-|Gypi2|--- Qubit 1 ---| |-| |--- 0.0105140.001904
Qubit 0 ---| |-| |--- Qubit 1 ---|Gxpi2|-|Gypi2|--- 0.0082990.001254
Qubit 0 ---|Gxpi2|-|Gxpi2|-|Gypi2|--- Qubit 1 ---| |-| |-| |--- 0.0122250.001578
Qubit 0 ---| |-| |-| |--- Qubit 1 ---|Gxpi2|-|Gxpi2|-|Gypi2|--- 0.0097570.001532
Qubit 0 ---| |-| |-|C1|--- Qubit 1 ---|Gxpi2|-|Gypi2|-|C0|--- 0.0249560.003869
Qubit 0 ---|C1|-| |-|Gxpi2|-|Gxpi2|--- Qubit 1 ---|C0|-|Gxpi2|-| |-| |--- 0.0110290.004865
Qubit 0 ---|Gxpi2|-| |-| |-|Gxpi2|-| |-|Gypi2|--- Qubit 1 ---| |-|Gxpi2|-|Gypi2|-| |-|Gypi2|-| |--- 0.0245390.00877
Qubit 0 ---|Gxpi2|-| |-| |-|Gypi2|-| |-| |--- Qubit 1 ---| |-|Gypi2|-|Gxpi2|-| |-|Gxpi2|-|Gxpi2|--- 0.0129570.003363
Qubit 0 ---|C1|-| |-|Gypi2|-|C1|-| |-|Gxpi2|--- Qubit 1 ---|C0|-|Gxpi2|-| |-|C0|-|Gypi2|-| |--- 0.0501090.006693
Qubit 0 ---|Gypi2|-|Gxpi2|-| |-|Gxpi2|-| |-|Gxpi2|-|Gypi2|-| |--- Qubit 1 ---| |-| |-|Gypi2|-| |-|Gxpi2|-| |-| |-|Gypi2|--- 0.0134490.004776
Gate or Germ Eigenvalue 1/2 Diamond-Dist Eigenvalue Non-U. 1/2 Diamond-Dist
[]00
Gxpi2:100
Gxpi2:000
Gypi2:100
Gypi2:000
Gcphase:0:100
Qubit 0 ---|Gxpi2|-|Gypi2|--- Qubit 1 ---| |-| |--- 0.0199530.003005
Qubit 0 ---| |-| |--- Qubit 1 ---|Gxpi2|-|Gypi2|--- 0.0097370.008516
Qubit 0 ---|Gxpi2|-|Gxpi2|-|Gypi2|--- Qubit 1 ---| |-| |-| |--- 0.0260280.003653
Qubit 0 ---| |-| |-| |--- Qubit 1 ---|Gxpi2|-|Gxpi2|-|Gypi2|--- 0.0173170.004963
Qubit 0 ---| |-| |-|C1|--- Qubit 1 ---|Gxpi2|-|Gypi2|-|C0|--- 0.0281330.000847
Qubit 0 ---|C1|-| |-|Gxpi2|-|Gxpi2|--- Qubit 1 ---|C0|-|Gxpi2|-| |-| |--- 0.0224010.008463
Qubit 0 ---|Gxpi2|-| |-| |-|Gxpi2|-| |-|Gypi2|--- Qubit 1 ---| |-|Gxpi2|-|Gypi2|-| |-|Gypi2|-| |--- 0.0375550.019163
Qubit 0 ---|Gxpi2|-| |-| |-|Gypi2|-| |-| |--- Qubit 1 ---| |-|Gypi2|-|Gxpi2|-| |-|Gxpi2|-|Gxpi2|--- 0.0160090.001262
Qubit 0 ---|C1|-| |-|Gypi2|-|C1|-| |-|Gxpi2|--- Qubit 1 ---|C0|-|Gxpi2|-| |-|C0|-|Gypi2|-| |--- 0.0432320.022142
Qubit 0 ---|Gypi2|-|Gxpi2|-| |-|Gxpi2|-| |-|Gxpi2|-|Gypi2|-| |--- Qubit 1 ---| |-| |-|Gypi2|-| |-|Gxpi2|-| |-| |-|Gypi2|--- 0.0142940.00939
Gate or Germ Eigenvalue 1/2 Diamond-Dist Eigenvalue Non-U. 1/2 Diamond-Dist
[]00
Gxpi2:100
Gxpi2:000
Gypi2:100
Gypi2:000
Gcphase:0:100
Qubit 0 ---|Gxpi2|-|Gypi2|--- Qubit 1 ---| |-| |--- 00
Qubit 0 ---| |-| |--- Qubit 1 ---|Gxpi2|-|Gypi2|--- 00
Qubit 0 ---|Gxpi2|-|Gxpi2|-|Gypi2|--- Qubit 1 ---| |-| |-| |--- 00
Qubit 0 ---| |-| |-| |--- Qubit 1 ---|Gxpi2|-|Gxpi2|-|Gypi2|--- 00
Qubit 0 ---| |-| |-|C1|--- Qubit 1 ---|Gxpi2|-|Gypi2|-|C0|--- 00
Qubit 0 ---|C1|-| |-|Gxpi2|-|Gxpi2|--- Qubit 1 ---|C0|-|Gxpi2|-| |-| |--- 00
Qubit 0 ---|Gxpi2|-| |-| |-|Gxpi2|-| |-|Gypi2|--- Qubit 1 ---| |-|Gxpi2|-|Gypi2|-| |-|Gypi2|-| |--- 00
Qubit 0 ---|Gxpi2|-| |-| |-|Gypi2|-| |-| |--- Qubit 1 ---| |-|Gypi2|-|Gxpi2|-| |-|Gxpi2|-|Gxpi2|--- 00
Qubit 0 ---|C1|-| |-|Gypi2|-|C1|-| |-|Gxpi2|--- Qubit 1 ---|C0|-|Gxpi2|-| |-|C0|-|Gypi2|-| |--- 00
Qubit 0 ---|Gypi2|-|Gxpi2|-| |-|Gxpi2|-| |-|Gxpi2|-|Gypi2|-| |--- Qubit 1 ---| |-| |-|Gypi2|-| |-|Gxpi2|-| |-| |-|Gypi2|--- 00
Eigenvalues of estimated germs. GST directly estimates each gate's spectrum (it's gauge-invariant), But the gates' eigenbases are relational to other gates and gauge-variant. GST infers them from the spectra of germs that incorporate multiple gates. Each germ's spectrum is gauge-invariant and directly estimatable, and this table lists them. It also lists metrics that compare these spectra to the ones predicted by the eigenspace-projected gates (see elsewhere on this tab). If the individual gates' eigenvalues account for all imperfections, then the estimated and predicted germ spectra should be equal. Since spectra aren't ordered, the eigenvalues need to be matched up or aligned somehow. PyGSTi does this by identifying a minimum-weight matching based on the metric being computed. Mathematical descriptions of the metrics appear when hovering over the column headers.
Gate or Germ Eigenvalues ($E$) Target Evals. ($T$) $|E - T|$ $1.0 - \mathrm{Re}(\bar{T}\cdot E)$ $\mathrm{Re} \log(E)$ $\mathrm{Im} \log(E)$ $|\mathrm{Re}(\log E) - \mathrm{Re}(\log T)|$ $|\mathrm{Im}(\log E) - \mathrm{Im}(\log T)|$
[]$ \begin{pmatrix} 1 \\ 0.996791 \\ 0.996531e^{i0.005\pi} \\ 0.996531e^{-i0.005\pi} \\ 0.995803e^{i0.002\pi} \\ 0.995803e^{-i0.002\pi} \\ 0.995384e^{i0.002\pi} \\ 0.995384e^{-i0.002\pi} \\ 0.99524e^{i0.004\pi} \\ 0.99524e^{-i0.004\pi} \\ 0.994699e^{i0.000\pi} \\ 0.994699e^{-i0.000\pi} \\ 0.994608e^{i0.001\pi} \\ 0.994608e^{-i0.001\pi} \\ 0.993456e^{i0.002\pi} \\ 0.993456e^{-i0.002\pi} \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.015809 \\ 0.033197e^{i0.127\pi} \\ 0.033197e^{i0.127\pi} \\ 0.06558e^{i0.106\pi} \\ 0.06558e^{i0.106\pi} \\ 0.08755e^{i0.308\pi} \\ 0.08755e^{i0.308\pi} \\ 0.047392e^{i0.128\pi} \\ 0.047392e^{i0.128\pi} \\ 0.088316e^{i0.181\pi} \\ 0.088316e^{i0.181\pi} \\ 0.104669e^{i0.227\pi} \\ 0.104669e^{i0.227\pi} \\ 0.082095e^{i0.329\pi} \\ 0.082095e^{i0.329\pi} \end{pmatrix} $ $ \begin{pmatrix} 1 \\ 0.996791 \\ 0.996531e^{i0.005\pi} \\ 0.996531e^{-i0.005\pi} \\ 0.995803e^{i0.002\pi} \\ 0.995803e^{-i0.002\pi} \\ 0.995384e^{i0.002\pi} \\ 0.995384e^{-i0.002\pi} \\ 0.99524e^{i0.004\pi} \\ 0.99524e^{-i0.004\pi} \\ 0.994699e^{i0.000\pi} \\ 0.994699e^{-i0.000\pi} \\ 0.994608e^{i0.001\pi} \\ 0.994608e^{-i0.001\pi} \\ 0.993456e^{i0.002\pi} \\ 0.993456e^{-i0.002\pi} \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.015809 \\ 0.033197 \\ 0.033197 \\ 0.06558 \\ 0.06558 \\ 0.08755 \\ 0.08755 \\ 0.047392 \\ 0.047392 \\ 0.088316 \\ 0.088316 \\ 0.104669 \\ 0.104669 \\ 0.082095 \\ 0.082095 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.006408 \\ 0.006925 \\ 0.006925 \\ 0.008376 \\ 0.008376 \\ 0.009211 \\ 0.009211 \\ 0.009497 \\ 0.009497 \\ 0.010573 \\ 0.010573 \\ 0.010755 \\ 0.010755 \\ 0.013046 \\ 0.013046 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.015758 \\ 0.030944 \\ 0.030037 \\ 0.062128 \\ 0.061308 \\ 0.04979 \\ 0.049045 \\ 0.043918 \\ 0.042858 \\ 0.074048 \\ 0.073951 \\ 0.07887 \\ 0.078457 \\ 0.04212 \\ 0.041515 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ -0.003214 \\ -0.003475 \\ -0.003475 \\ -0.004206 \\ -0.004206 \\ -0.004627 \\ -0.004627 \\ -0.004771 \\ -0.004771 \\ -0.005315 \\ -0.005315 \\ -0.005407 \\ -0.005407 \\ -0.006566 \\ -0.006566 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.015735 \\ 0.030501 \\ 0.030139 \\ 0.060711 \\ 0.060458 \\ 0.051541 \\ 0.050554 \\ 0.043241 \\ 0.042822 \\ 0.073142 \\ 0.073088 \\ 0.078704 \\ 0.078395 \\ 0.044278 \\ 0.043338 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0.004737 \\ -0.004737 \\ 0.002115 \\ -0.002115 \\ 0.002401 \\ -0.002401 \\ 0.003891 \\ -0.003891 \\ 0.000208 \\ -0.000208 \\ 0.000835 \\ -0.000835 \\ 0.002301 \\ -0.002301 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0.003847 \\ 0.00413 \\ 0.006323 \\ 0.006572 \\ 0.021804 \\ 0.022054 \\ 0.005527 \\ 0.005856 \\ 0.014147 \\ 0.014177 \\ 0.020233 \\ 0.020362 \\ 0.021527 \\ 0.021735 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.015735 \\ 0.030501 \\ 0.030139 \\ 0.060711 \\ 0.060458 \\ 0.051541 \\ 0.050554 \\ 0.043241 \\ 0.042822 \\ 0.073142 \\ 0.073088 \\ 0.078704 \\ 0.078395 \\ 0.044278 \\ 0.043338 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0.003847 \\ 0.00413 \\ 0.006323 \\ 0.006572 \\ 0.021804 \\ 0.022054 \\ 0.005527 \\ 0.005856 \\ 0.014147 \\ 0.014177 \\ 0.020233 \\ 0.020362 \\ 0.021527 \\ 0.021735 \end{pmatrix} $ π
Gxpi2:1$ \begin{pmatrix} 1 \\ 0.997483e^{i0.498\pi} \\ 0.997483e^{-i0.498\pi} \\ 0.997246e^{i0.499\pi} \\ 0.997246e^{-i0.499\pi} \\ 0.996617 \\ 0.996347 \\ 0.996066e^{i0.002\pi} \\ 0.996066e^{-i0.002\pi} \\ 0.995239e^{i0.002\pi} \\ 0.995239e^{-i0.002\pi} \\ 0.994789e^{i0.500\pi} \\ 0.994789e^{-i0.500\pi} \\ 0.994209e^{i0.501\pi} \\ 0.994209e^{-i0.501\pi} \\ 0.992407 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.013116e^{i0.286\pi} \\ 0.013116e^{i0.286\pi} \\ 0.012005e^{i0.190\pi} \\ 0.012005e^{i0.190\pi} \\ 0.036209 \\ 0.019967 \\ 0.025786e^{i0.090\pi} \\ 0.025786e^{i0.090\pi} \\ 0.024928e^{i0.343\pi} \\ 0.024928e^{i0.343\pi} \\ 0.011678e^{i0.195\pi} \\ 0.011678e^{i0.195\pi} \\ 0.013669e^{i0.278\pi} \\ 0.013669e^{i0.278\pi} \\ 0.012952 \end{pmatrix} $ $ \begin{pmatrix} 1 \\ 0.997483e^{i0.498\pi} \\ 0.997483e^{-i0.498\pi} \\ 0.997246e^{i0.499\pi} \\ 0.997246e^{-i0.499\pi} \\ 0.996617 \\ 0.996347 \\ 0.996066e^{i0.002\pi} \\ 0.996066e^{-i0.002\pi} \\ 0.995239e^{i0.002\pi} \\ 0.995239e^{-i0.002\pi} \\ 0.994789e^{i0.500\pi} \\ 0.994789e^{-i0.500\pi} \\ 0.994209e^{i0.501\pi} \\ 0.994209e^{-i0.501\pi} \\ 0.992407 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.013116 \\ 0.013116 \\ 0.012005 \\ 0.012005 \\ 0.036209 \\ 0.019967 \\ 0.025786 \\ 0.025786 \\ 0.024928 \\ 0.024928 \\ 0.011678 \\ 0.011678 \\ 0.013669 \\ 0.013669 \\ 0.012952 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.005028 \\ 0.005028 \\ 0.005501 \\ 0.005501 \\ 0.006755 \\ 0.007292 \\ 0.007853 \\ 0.007853 \\ 0.0095 \\ 0.0095 \\ 0.010395 \\ 0.010395 \\ 0.011548 \\ 0.011548 \\ 0.015128 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.008203 \\ 0.008098 \\ 0.009909 \\ 0.009877 \\ 0.036087 \\ 0.019894 \\ 0.024787 \\ 0.024552 \\ 0.0118 \\ 0.011675 \\ 0.0095 \\ 0.009493 \\ 0.008703 \\ 0.008764 \\ 0.012854 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ -0.00252 \\ -0.00252 \\ -0.002758 \\ -0.002758 \\ -0.003389 \\ -0.003659 \\ -0.003942 \\ -0.003942 \\ -0.004773 \\ -0.004773 \\ -0.005225 \\ -0.005225 \\ -0.005807 \\ -0.005807 \\ -0.007622 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.010317 \\ -0.01025 \\ 0.006821 \\ -0.006736 \\ 0.035688 \\ 0.019842 \\ 0.024618 \\ 0.024553 \\ 0.012133 \\ 0.011903 \\ 0.006788 \\ -0.006734 \\ 0.010485 \\ -0.010581 \\ 0.012967 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.497954 \\ -0.497954 \\ 0.499491 \\ -0.499491 \\ 0 \\ 0 \\ 0.001515 \\ -0.001515 \\ 0.001696 \\ -0.001696 \\ 0.499883 \\ -0.499883 \\ 0.501122 \\ -0.501122 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ -0.00256 \\ 0.002656 \\ -0.003142 \\ 0.003191 \\ 0 \\ 0 \\ 0.002201 \\ 0.002275 \\ 0.00692 \\ 0.006961 \\ -0.003033 \\ 0.003076 \\ -0.002795 \\ 0.00283 \\ 0 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.010317 \\ 0.01025 \\ 0.006821 \\ 0.006736 \\ 0.035688 \\ 0.019842 \\ 0.024618 \\ 0.024553 \\ 0.012133 \\ 0.011903 \\ 0.006788 \\ 0.006734 \\ 0.010485 \\ 0.010581 \\ 0.012967 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0.00256 \\ 0.002656 \\ 0.003142 \\ 0.003191 \\ 0 \\ 0 \\ 0.002201 \\ 0.002275 \\ 0.00692 \\ 0.006961 \\ 0.003033 \\ 0.003076 \\ 0.002795 \\ 0.00283 \\ 0 \end{pmatrix} $ π
Gxpi2:0$ \begin{pmatrix} 1 \\ 0.997502 \\ 0.996375e^{i0.503\pi} \\ 0.996375e^{-i0.503\pi} \\ 0.996167e^{i0.502\pi} \\ 0.996167e^{-i0.502\pi} \\ 0.995741 \\ 0.993843 \\ 0.993534e^{i0.512\pi} \\ 0.993534e^{-i0.512\pi} \\ 0.993398e^{i0.009\pi} \\ 0.993398e^{-i0.009\pi} \\ 0.992042e^{i0.010\pi} \\ 0.992042e^{-i0.010\pi} \\ 0.991391e^{i0.493\pi} \\ 0.991391e^{-i0.493\pi} \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.006834 \\ 0.009491e^{i0.149\pi} \\ 0.009491e^{i0.149\pi} \\ 0.010889e^{i0.135\pi} \\ 0.010889e^{i0.135\pi} \\ 0.005753 \\ 0.017147 \\ 0.035739e^{i0.334\pi} \\ 0.035739e^{i0.334\pi} \\ 0.018055e^{i0.326\pi} \\ 0.018055e^{i0.326\pi} \\ 0.038498e^{i0.377\pi} \\ 0.038498e^{i0.377\pi} \\ 0.030343e^{i0.369\pi} \\ 0.030343e^{i0.369\pi} \end{pmatrix} $ $ \begin{pmatrix} 1 \\ 0.997502 \\ 0.996375e^{i0.503\pi} \\ 0.996375e^{-i0.503\pi} \\ 0.996167e^{i0.502\pi} \\ 0.996167e^{-i0.502\pi} \\ 0.995741 \\ 0.993843 \\ 0.993534e^{i0.512\pi} \\ 0.993534e^{-i0.512\pi} \\ 0.993398e^{i0.009\pi} \\ 0.993398e^{-i0.009\pi} \\ 0.992042e^{i0.010\pi} \\ 0.992042e^{-i0.010\pi} \\ 0.991391e^{i0.493\pi} \\ 0.991391e^{-i0.493\pi} \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.006834 \\ 0.009491 \\ 0.009491 \\ 0.010889 \\ 0.010889 \\ 0.005753 \\ 0.017147 \\ 0.035739 \\ 0.035739 \\ 0.018055 \\ 0.018055 \\ 0.038498 \\ 0.038498 \\ 0.030343 \\ 0.030343 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.00499 \\ 0.007237 \\ 0.007237 \\ 0.00765 \\ 0.00765 \\ 0.008501 \\ 0.012277 \\ 0.01289 \\ 0.01289 \\ 0.013161 \\ 0.013161 \\ 0.015853 \\ 0.015853 \\ 0.017144 \\ 0.017144 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.006817 \\ 0.008354 \\ 0.008529 \\ 0.009816 \\ 0.009946 \\ 0.005729 \\ 0.017042 \\ 0.016954 \\ 0.018308 \\ 0.009575 \\ 0.00904 \\ 0.014781 \\ 0.013893 \\ 0.012308 \\ 0.011771 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ -0.002501 \\ -0.003632 \\ -0.003632 \\ -0.00384 \\ -0.00384 \\ -0.004269 \\ -0.006176 \\ -0.006487 \\ -0.006487 \\ -0.006624 \\ -0.006624 \\ -0.00799 \\ -0.00799 \\ -0.008646 \\ -0.008646 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.006828 \\ 0.004231 \\ -0.004353 \\ 0.004484 \\ -0.004535 \\ 0.005761 \\ 0.017106 \\ 0.030222 \\ -0.03225 \\ 0.009944 \\ 0.009068 \\ 0.01617 \\ 0.01401 \\ 0.027984 \\ -0.028072 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0.503296 \\ -0.503296 \\ 0.502085 \\ -0.502085 \\ 0 \\ 0 \\ 0.512221 \\ -0.512221 \\ 0.009152 \\ -0.009152 \\ 0.009854 \\ -0.009854 \\ 0.492896 \\ -0.492896 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ -0.002709 \\ 0.002704 \\ -0.003165 \\ 0.003175 \\ 0 \\ 0 \\ -0.005886 \\ 0.005478 \\ 0.004808 \\ 0.004984 \\ 0.01112 \\ 0.011427 \\ -0.003598 \\ 0.004215 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.006828 \\ 0.004231 \\ 0.004353 \\ 0.004484 \\ 0.004535 \\ 0.005761 \\ 0.017106 \\ 0.030222 \\ 0.03225 \\ 0.009944 \\ 0.009068 \\ 0.01617 \\ 0.01401 \\ 0.027984 \\ 0.028072 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0.002709 \\ 0.002704 \\ 0.003165 \\ 0.003175 \\ 0 \\ 0 \\ 0.005886 \\ 0.005478 \\ 0.004808 \\ 0.004984 \\ 0.01112 \\ 0.011427 \\ 0.003598 \\ 0.004215 \end{pmatrix} $ π
Gypi2:1$ \begin{pmatrix} 1 \\ 0.996262 \\ 0.995668e^{i0.501\pi} \\ 0.995668e^{-i0.501\pi} \\ 0.994997e^{i0.005\pi} \\ 0.994997e^{-i0.005\pi} \\ 0.994226e^{i0.008\pi} \\ 0.994226e^{-i0.008\pi} \\ 0.99416e^{i0.494\pi} \\ 0.99416e^{-i0.494\pi} \\ 0.993345 \\ 0.991749 \\ 0.990751e^{i0.506\pi} \\ 0.990751e^{-i0.506\pi} \\ 0.990126e^{i0.499\pi} \\ 0.990126e^{-i0.499\pi} \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.011409 \\ 0.013921e^{i0.147\pi} \\ 0.013921e^{i0.147\pi} \\ 0.020085e^{i0.333\pi} \\ 0.020085e^{i0.333\pi} \\ 0.02497e^{i0.247\pi} \\ 0.02497e^{i0.247\pi} \\ 0.006584e^{i0.249\pi} \\ 0.006584e^{i0.249\pi} \\ 0.042272 \\ 0.038761 \\ 0.038939e^{i0.081\pi} \\ 0.038939e^{i0.081\pi} \\ 0.01071e^{i0.226\pi} \\ 0.01071e^{i0.226\pi} \end{pmatrix} $ $ \begin{pmatrix} 1 \\ 0.996262 \\ 0.995668e^{i0.501\pi} \\ 0.995668e^{-i0.501\pi} \\ 0.994997e^{i0.005\pi} \\ 0.994997e^{-i0.005\pi} \\ 0.994226e^{i0.008\pi} \\ 0.994226e^{-i0.008\pi} \\ 0.99416e^{i0.494\pi} \\ 0.99416e^{-i0.494\pi} \\ 0.993345 \\ 0.991749 \\ 0.990751e^{i0.506\pi} \\ 0.990751e^{-i0.506\pi} \\ 0.990126e^{i0.499\pi} \\ 0.990126e^{-i0.499\pi} \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.011409 \\ 0.013921 \\ 0.013921 \\ 0.020085 \\ 0.020085 \\ 0.02497 \\ 0.02497 \\ 0.006584 \\ 0.006584 \\ 0.042272 \\ 0.038761 \\ 0.038939 \\ 0.038939 \\ 0.01071 \\ 0.01071 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.007462 \\ 0.008646 \\ 0.008646 \\ 0.009981 \\ 0.009981 \\ 0.011516 \\ 0.011516 \\ 0.011646 \\ 0.011646 \\ 0.013266 \\ 0.016435 \\ 0.018413 \\ 0.018413 \\ 0.01965 \\ 0.01965 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.011366 \\ 0.012371 \\ 0.012443 \\ 0.010169 \\ 0.009863 \\ 0.018175 \\ 0.017302 \\ 0.004726 \\ 0.004549 \\ 0.04199 \\ 0.038441 \\ 0.036639 \\ 0.038033 \\ 0.008067 \\ 0.00803 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ -0.003745 \\ -0.004342 \\ -0.004342 \\ -0.005016 \\ -0.005016 \\ -0.005791 \\ -0.005791 \\ -0.005857 \\ -0.005857 \\ -0.006677 \\ -0.008286 \\ -0.009293 \\ -0.009293 \\ -0.009923 \\ -0.009923 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.011387 \\ 0.006256 \\ -0.00621 \\ 0.010477 \\ 0.009955 \\ 0.018352 \\ 0.017518 \\ 0.004761 \\ -0.004581 \\ 0.041674 \\ 0.038339 \\ 0.009831 \\ -0.009901 \\ 0.007071 \\ -0.007015 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0.500922 \\ -0.500922 \\ 0.004855 \\ -0.004855 \\ 0.007834 \\ -0.007834 \\ 0.493908 \\ -0.493908 \\ 0 \\ 0 \\ 0.505942 \\ -0.505942 \\ 0.499257 \\ -0.499257 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ -0.003965 \\ 0.004003 \\ 0.005453 \\ 0.005553 \\ 0.00535 \\ 0.005631 \\ -0.001458 \\ 0.001529 \\ 0 \\ 0 \\ -0.01205 \\ 0.012172 \\ -0.00259 \\ 0.002637 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.011387 \\ 0.006256 \\ 0.00621 \\ 0.010477 \\ 0.009955 \\ 0.018352 \\ 0.017518 \\ 0.004761 \\ 0.004581 \\ 0.041674 \\ 0.038339 \\ 0.009831 \\ 0.009901 \\ 0.007071 \\ 0.007015 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0.003965 \\ 0.004003 \\ 0.005453 \\ 0.005553 \\ 0.00535 \\ 0.005631 \\ 0.001458 \\ 0.001529 \\ 0 \\ 0 \\ 0.01205 \\ 0.012172 \\ 0.00259 \\ 0.002637 \end{pmatrix} $ π
Gypi2:0$ \begin{pmatrix} 1 \\ 0.995519e^{i0.000\pi} \\ 0.995519e^{-i0.000\pi} \\ 0.995479e^{i0.501\pi} \\ 0.995479e^{-i0.501\pi} \\ 0.993242e^{i0.502\pi} \\ 0.993242e^{-i0.502\pi} \\ 0.99117 \\ 0.987858e^{i0.014\pi} \\ 0.987858e^{-i0.014\pi} \\ 0.987177e^{i0.515\pi} \\ 0.987177e^{-i0.515\pi} \\ 0.984056e^{i0.489\pi} \\ 0.984056e^{-i0.489\pi} \\ 0.982904e^{i0.011\pi} \\ 0.982904e^{-i0.011\pi} \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.016552e^{i0.352\pi} \\ 0.016552e^{i0.352\pi} \\ 0.009933e^{i0.202\pi} \\ 0.009933e^{i0.202\pi} \\ 0.016999e^{i0.132\pi} \\ 0.016999e^{i0.132\pi} \\ 0.023078 \\ 0.004973e^{i0.076\pi} \\ 0.004973e^{i0.076\pi} \\ 0.03488e^{i0.248\pi} \\ 0.03488e^{i0.248\pi} \\ 0.030281e^{i0.308\pi} \\ 0.030281e^{i0.308\pi} \\ 0.044571e^{i0.343\pi} \\ 0.044571e^{i0.343\pi} \end{pmatrix} $ $ \begin{pmatrix} 1 \\ 0.995519e^{i0.000\pi} \\ 0.995519e^{-i0.000\pi} \\ 0.995479e^{i0.501\pi} \\ 0.995479e^{-i0.501\pi} \\ 0.993242e^{i0.502\pi} \\ 0.993242e^{-i0.502\pi} \\ 0.99117 \\ 0.987858e^{i0.014\pi} \\ 0.987858e^{-i0.014\pi} \\ 0.987177e^{i0.515\pi} \\ 0.987177e^{-i0.515\pi} \\ 0.984056e^{i0.489\pi} \\ 0.984056e^{-i0.489\pi} \\ 0.982904e^{i0.011\pi} \\ 0.982904e^{-i0.011\pi} \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.016552 \\ 0.016552 \\ 0.009933 \\ 0.009933 \\ 0.016999 \\ 0.016999 \\ 0.023078 \\ 0.004973 \\ 0.004973 \\ 0.03488 \\ 0.03488 \\ 0.030281 \\ 0.030281 \\ 0.044571 \\ 0.044571 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.008942 \\ 0.008942 \\ 0.009021 \\ 0.009021 \\ 0.01347 \\ 0.01347 \\ 0.017582 \\ 0.024138 \\ 0.024138 \\ 0.025482 \\ 0.025482 \\ 0.031633 \\ 0.031633 \\ 0.0339 \\ 0.0339 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.007401 \\ 0.007394 \\ 0.007934 \\ 0.007984 \\ 0.015354 \\ 0.015539 \\ 0.022874 \\ 0.004981 \\ 0.00456 \\ 0.023357 \\ 0.025604 \\ 0.017488 \\ 0.016354 \\ 0.021451 \\ 0.019999 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ -0.004491 \\ -0.004491 \\ -0.004531 \\ -0.004531 \\ -0.006781 \\ -0.006781 \\ -0.008869 \\ -0.012217 \\ -0.012217 \\ -0.012906 \\ -0.012906 \\ -0.016072 \\ -0.016072 \\ -0.017244 \\ -0.017244 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.007552 \\ 0.007539 \\ 0.005911 \\ -0.005932 \\ 0.006915 \\ -0.006904 \\ 0.023016 \\ 0.004929 \\ 0.004826 \\ 0.023696 \\ -0.025988 \\ 0.025696 \\ -0.024857 \\ 0.023327 \\ 0.020649 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.000148 \\ -0.000148 \\ 0.501012 \\ -0.501012 \\ 0.501897 \\ -0.501897 \\ 0 \\ 0.014014 \\ -0.014014 \\ 0.514598 \\ -0.514598 \\ 0.489335 \\ -0.489335 \\ 0.011148 \\ -0.011148 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0.004693 \\ 0.004695 \\ -0.002547 \\ 0.002566 \\ -0.004963 \\ 0.005005 \\ 0 \\ 0.000307 \\ 0.000443 \\ -0.008163 \\ 0.007836 \\ -0.005158 \\ 0.005979 \\ 0.012183 \\ 0.012685 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.007552 \\ 0.007539 \\ 0.005911 \\ 0.005932 \\ 0.006915 \\ 0.006904 \\ 0.023016 \\ 0.004929 \\ 0.004826 \\ 0.023696 \\ 0.025988 \\ 0.025696 \\ 0.024857 \\ 0.023327 \\ 0.020649 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0.004693 \\ 0.004695 \\ 0.002547 \\ 0.002566 \\ 0.004963 \\ 0.005005 \\ 0 \\ 0.000307 \\ 0.000443 \\ 0.008163 \\ 0.007836 \\ 0.005158 \\ 0.005979 \\ 0.012183 \\ 0.012685 \end{pmatrix} $ π
Gcphase:0:1$ \begin{pmatrix} 1 \\ 0.996117 \\ 0.983788e^{i0.009\pi} \\ 0.983788e^{-i0.009\pi} \\ 0.983255e^{i0.983\pi} \\ 0.983255e^{-i0.983\pi} \\ 0.979147e^{i0.001\pi} \\ 0.979147e^{-i0.001\pi} \\ 0.976084e^{i0.016\pi} \\ 0.976084e^{-i0.016\pi} \\ 0.971781e^{i0.007\pi} \\ 0.971781e^{-i0.007\pi} \\ 0.97097e^{i0.993\pi} \\ 0.97097e^{-i0.993\pi} \\ 0.957648e^{i0.976\pi} \\ 0.957648e^{-i0.976\pi} \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.00159 \\ 0.057165e^{i0.337\pi} \\ 0.057165e^{i0.337\pi} \\ 0.016817e^{i0.290\pi} \\ 0.016817e^{i0.290\pi} \\ 0.025934e^{i0.183\pi} \\ 0.025934e^{i0.183\pi} \\ 0.045487e^{i0.269\pi} \\ 0.045487e^{i0.269\pi} \\ 0.073076e^{i0.319\pi} \\ 0.073076e^{i0.319\pi} \\ 0.026551e^{i0.378\pi} \\ 0.026551e^{i0.378\pi} \\ 0.021225e^{i0.085\pi} \\ 0.021225e^{i0.085\pi} \end{pmatrix} $ $ \begin{pmatrix} 1 \\ 0.996117 \\ 0.983788e^{i0.009\pi} \\ 0.983788e^{-i0.009\pi} \\ 0.983255e^{i0.983\pi} \\ 0.983255e^{-i0.983\pi} \\ 0.979147e^{i0.001\pi} \\ 0.979147e^{-i0.001\pi} \\ 0.976084e^{i0.016\pi} \\ 0.976084e^{-i0.016\pi} \\ 0.971781e^{i0.007\pi} \\ 0.971781e^{-i0.007\pi} \\ 0.97097e^{i0.993\pi} \\ 0.97097e^{-i0.993\pi} \\ 0.957648e^{i0.976\pi} \\ 0.957648e^{-i0.976\pi} \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.00159 \\ 0.057165 \\ 0.057165 \\ 0.016817 \\ 0.016817 \\ 0.025934 \\ 0.025934 \\ 0.045487 \\ 0.045487 \\ 0.073076 \\ 0.073076 \\ 0.026551 \\ 0.026551 \\ 0.021225 \\ 0.021225 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.00775 \\ 0.032161 \\ 0.032161 \\ 0.03321 \\ 0.03321 \\ 0.041272 \\ 0.041272 \\ 0.047259 \\ 0.047259 \\ 0.055642 \\ 0.055642 \\ 0.057218 \\ 0.057218 \\ 0.08291 \\ 0.08291 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.001584 \\ 0.028407 \\ 0.026784 \\ 0.00958 \\ 0.01065 \\ 0.021377 \\ 0.021259 \\ 0.03091 \\ 0.027901 \\ 0.039117 \\ 0.037439 \\ 0.009404 \\ 0.009809 \\ 0.018044 \\ 0.021054 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ -0.00389 \\ -0.016345 \\ -0.016345 \\ -0.016887 \\ -0.016887 \\ -0.021074 \\ -0.021074 \\ -0.024206 \\ -0.024206 \\ -0.028625 \\ -0.028625 \\ -0.02946 \\ -0.02946 \\ -0.043275 \\ -0.043275 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.001595 \\ 0.030725 \\ 0.027918 \\ -0.009696 \\ -0.011153 \\ 0.02213 \\ 0.022053 \\ 0.032644 \\ 0.029292 \\ 0.042858 \\ 0.040304 \\ -0.009368 \\ -0.010459 \\ -0.021059 \\ -0.021996 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0.009356 \\ -0.009356 \\ 0.98319 \\ -0.98319 \\ 0.000884 \\ -0.000884 \\ 0.016277 \\ -0.016277 \\ 0.006976 \\ -0.006976 \\ 0.99329 \\ -0.99329 \\ 0.975543 \\ -0.975543 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0.015367 \\ 0.01593 \\ -0.004517 \\ -0.004167 \\ 0.004461 \\ 0.0045 \\ 0.010247 \\ 0.011259 \\ 0.019049 \\ 0.019642 \\ -0.008221 \\ 1.991908 \\ -0.002428 \\ -0.001362 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.001595 \\ 0.030725 \\ 0.027918 \\ 0.009696 \\ 0.011153 \\ 0.02213 \\ 0.022053 \\ 0.032644 \\ 0.029292 \\ 0.042858 \\ 0.040304 \\ 0.009368 \\ 0.010459 \\ 0.021059 \\ 0.021996 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0.015367 \\ 0.01593 \\ 0.004517 \\ 0.004167 \\ 0.004461 \\ 0.0045 \\ 0.010247 \\ 0.011259 \\ 0.019049 \\ 0.019642 \\ 0.008221 \\ 1.991908 \\ 0.002428 \\ 0.001362 \end{pmatrix} $ π
Qubit 0 ---|Gxpi2|-|Gypi2|--- Qubit 1 ---| |-| |--- $ \begin{pmatrix} 1 \\ 0.993372 \\ 0.992175e^{i0.672\pi} \\ 0.992175e^{-i0.672\pi} \\ 0.989373 \\ 0.987761e^{i0.672\pi} \\ 0.987761e^{-i0.672\pi} \\ 0.986442 \\ 0.982177e^{i0.022\pi} \\ 0.982177e^{-i0.022\pi} \\ 0.978777e^{i0.695\pi} \\ 0.978777e^{-i0.695\pi} \\ 0.977417e^{i0.650\pi} \\ 0.977417e^{-i0.650\pi} \\ 0.975866e^{i0.023\pi} \\ 0.975866e^{-i0.023\pi} \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.017752 \\ 0.023302e^{i0.232\pi} \\ 0.023302e^{i0.232\pi} \\ 0.008184 \\ 0.028139e^{i0.265\pi} \\ 0.028139e^{i0.265\pi} \\ 0.023689 \\ 0.035428e^{i0.307\pi} \\ 0.035428e^{i0.307\pi} \\ 0.066361e^{i0.302\pi} \\ 0.066361e^{i0.302\pi} \\ 0.063601e^{i0.287\pi} \\ 0.063601e^{i0.287\pi} \\ 0.046033e^{i0.276\pi} \\ 0.046033e^{i0.276\pi} \end{pmatrix} $ $ \begin{pmatrix} 1 \\ 0.992537 \\ 0.991889e^{i0.669\pi} \\ 0.991889e^{-i0.669\pi} \\ 0.990745 \\ 0.987882e^{i0.669\pi} \\ 0.987882e^{-i0.669\pi} \\ 0.987304 \\ 0.977682e^{i0.021\pi} \\ 0.977682e^{-i0.021\pi} \\ 0.979422e^{i0.691\pi} \\ 0.979422e^{-i0.691\pi} \\ 0.97645e^{i0.647\pi} \\ 0.97645e^{-i0.647\pi} \\ 0.980146e^{i0.023\pi} \\ 0.980146e^{-i0.023\pi} \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.000835 \\ 0.011215 \\ 0.011215 \\ 0.001371 \\ 0.008351 \\ 0.008351 \\ 0.000862 \\ 0.004906 \\ 0.004906 \\ 0.010227 \\ 0.010227 \\ 0.009968 \\ 0.009968 \\ 0.004291 \\ 0.004291 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.017752 \\ 0.023302 \\ 0.023302 \\ 0.008184 \\ 0.028139 \\ 0.028139 \\ 0.023689 \\ 0.035428 \\ 0.035428 \\ 0.066361 \\ 0.066361 \\ 0.063601 \\ 0.063601 \\ 0.046033 \\ 0.046033 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.014042 \\ 0.015935 \\ 0.015935 \\ 0.019783 \\ 0.024243 \\ 0.024243 \\ 0.026082 \\ 0.039745 \\ 0.039745 \\ 0.041416 \\ 0.041416 \\ 0.04565 \\ 0.04565 \\ 0.043509 \\ 0.043509 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.017619 \\ 0.006163 \\ 0.02362 \\ 0.008108 \\ 0.006642 \\ 0.025649 \\ 0.023388 \\ 0.020995 \\ 0.018359 \\ 0.00983 \\ 0.052727 \\ 0.017269 \\ 0.051625 \\ 0.03122 \\ 0.026996 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ -0.00665 \\ -0.007856 \\ -0.007856 \\ -0.010683 \\ -0.012315 \\ -0.012315 \\ -0.013651 \\ -0.017984 \\ -0.017984 \\ -0.021451 \\ -0.021451 \\ -0.022842 \\ -0.022842 \\ -0.02443 \\ -0.02443 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.017712 \\ 0.0046 \\ -0.022654 \\ 0.008238 \\ 0.0085 \\ -0.028305 \\ 0.023731 \\ 0.022659 \\ 0.018743 \\ 0.024079 \\ -0.070203 \\ 0.028395 \\ -0.065864 \\ 0.033022 \\ 0.028146 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0.672353 \\ -0.672353 \\ 0 \\ 0.672032 \\ -0.672032 \\ 0 \\ 0.021925 \\ -0.021925 \\ 0.69465 \\ -0.69465 \\ 0.650477 \\ -0.650477 \\ 0.022951 \\ -0.022951 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ -0.007314 \\ 0.002273 \\ 0 \\ -0.008615 \\ 0.001845 \\ 0 \\ 0.008767 \\ 0.009685 \\ -0.019901 \\ 0.000267 \\ -0.018314 \\ 0.004304 \\ 0.010375 \\ 0.011787 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0.000841 \\ 0.000289 \\ 0.000289 \\ 0.001385 \\ 0.000123 \\ 0.000123 \\ 0.000874 \\ 0.004587 \\ 0.004587 \\ 0.000658 \\ 0.000658 \\ 0.000991 \\ 0.000991 \\ 0.004376 \\ 0.004376 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.017712 \\ 0.0046 \\ 0.022654 \\ 0.008238 \\ 0.0085 \\ 0.028305 \\ 0.023731 \\ 0.022659 \\ 0.018743 \\ 0.024079 \\ 0.070203 \\ 0.028395 \\ 0.065864 \\ 0.033022 \\ 0.028146 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0.003597 \\ 0.003597 \\ 0 \\ 0.002691 \\ 0.002691 \\ 0 \\ 0.000638 \\ 0.000638 \\ 0.003318 \\ 0.003318 \\ 0.003232 \\ 0.003232 \\ 0.000101 \\ 0.000101 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0.007314 \\ 0.002273 \\ 0 \\ 0.008615 \\ 0.001845 \\ 0 \\ 0.008767 \\ 0.009685 \\ 0.019901 \\ 0.000267 \\ 0.018314 \\ 0.004304 \\ 0.010375 \\ 0.011787 \end{pmatrix} $ π
Qubit 0 ---| |-| |--- Qubit 1 ---|Gxpi2|-|Gypi2|--- $ \begin{pmatrix} 1 \\ 0.99239 \\ 0.991821e^{i0.669\pi} \\ 0.991821e^{-i0.669\pi} \\ 0.991379e^{i0.009\pi} \\ 0.991379e^{-i0.009\pi} \\ 0.990616 \\ 0.988792e^{i0.660\pi} \\ 0.988792e^{-i0.660\pi} \\ 0.988008e^{i0.002\pi} \\ 0.988008e^{-i0.002\pi} \\ 0.987666e^{i0.663\pi} \\ 0.987666e^{-i0.663\pi} \\ 0.986517e^{i0.673\pi} \\ 0.986517e^{-i0.673\pi} \\ 0.985684 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.02826 \\ 0.027822e^{i0.029\pi} \\ 0.027822e^{i0.029\pi} \\ 0.036253e^{i0.265\pi} \\ 0.036253e^{i0.265\pi} \\ 0.022415 \\ 0.056784e^{i0.344\pi} \\ 0.056784e^{i0.344\pi} \\ 0.033516e^{i0.208\pi} \\ 0.033516e^{i0.208\pi} \\ 0.032837e^{i0.222\pi} \\ 0.032837e^{i0.222\pi} \\ 0.068819e^{i0.110\pi} \\ 0.068819e^{i0.110\pi} \\ 0.049819 \end{pmatrix} $ $ \begin{pmatrix} 1 \\ 0.991675 \\ 0.991518e^{i0.667\pi} \\ 0.991518e^{-i0.667\pi} \\ 0.990041e^{i0.007\pi} \\ 0.990041e^{-i0.007\pi} \\ 0.990658 \\ 0.988753e^{i0.660\pi} \\ 0.988753e^{-i0.660\pi} \\ 0.989426e^{i0.005\pi} \\ 0.989426e^{-i0.005\pi} \\ 0.986856e^{i0.666\pi} \\ 0.986856e^{-i0.666\pi} \\ 0.987251e^{i0.673\pi} \\ 0.987251e^{-i0.673\pi} \\ 0.98702 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.000715 \\ 0.006861 \\ 0.006861 \\ 0.007367 \\ 0.007367 \\ 0.000042 \\ 0.0012 \\ 0.0012 \\ 0.008852 \\ 0.008852 \\ 0.008144 \\ 0.008144 \\ 0.000734 \\ 0.000734 \\ 0.001336 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.02826 \\ 0.027822 \\ 0.027822 \\ 0.036253 \\ 0.036253 \\ 0.022415 \\ 0.056784 \\ 0.056784 \\ 0.033516 \\ 0.033516 \\ 0.032837 \\ 0.032837 \\ 0.068819 \\ 0.068819 \\ 0.049819 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.015871 \\ 0.016615 \\ 0.016615 \\ 0.018521 \\ 0.018521 \\ 0.018638 \\ 0.022329 \\ 0.022329 \\ 0.022477 \\ 0.022477 \\ 0.025349 \\ 0.025349 \\ 0.02606 \\ 0.02606 \\ 0.02711 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.028025 \\ 0.010028 \\ 0.037538 \\ 0.024666 \\ 0.02359 \\ 0.022206 \\ 0.010394 \\ 0.035877 \\ 0.026745 \\ 0.025904 \\ 0.009172 \\ 0.033955 \\ 0.021753 \\ 0.087725 \\ 0.049172 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ -0.007639 \\ -0.008213 \\ -0.008213 \\ -0.008659 \\ -0.008659 \\ -0.009428 \\ -0.011271 \\ -0.011271 \\ -0.012064 \\ -0.012064 \\ -0.01241 \\ -0.01241 \\ -0.013575 \\ -0.013575 \\ -0.014419 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.028079 \\ -0.01172 \\ -0.016197 \\ 0.025392 \\ 0.023867 \\ 0.022375 \\ 0.032017 \\ -0.059137 \\ 0.026917 \\ 0.026637 \\ 0.006545 \\ -0.031517 \\ -0.011286 \\ -0.054588 \\ 0.049306 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0.669102 \\ -0.669102 \\ 0.009423 \\ -0.009423 \\ 0 \\ 0.659855 \\ -0.659855 \\ 0.002276 \\ -0.002276 \\ 0.663406 \\ -0.663406 \\ 0.672638 \\ -0.672638 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ -0.00817 \\ 0.007379 \\ 0.008171 \\ 0.008636 \\ 0 \\ -0.014825 \\ -0.000241 \\ 0.006332 \\ 0.006453 \\ -0.010341 \\ 0.003863 \\ -0.022044 \\ 0.014791 \\ 0 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0.000721 \\ 0.000305 \\ 0.000305 \\ 0.00135 \\ 0.00135 \\ 0.000042 \\ 0.000039 \\ 0.000039 \\ 0.001435 \\ 0.001435 \\ 0.000821 \\ 0.000821 \\ 0.000744 \\ 0.000744 \\ 0.001355 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.028079 \\ 0.01172 \\ 0.016197 \\ 0.025392 \\ 0.023867 \\ 0.022375 \\ 0.032017 \\ 0.059137 \\ 0.026917 \\ 0.026637 \\ 0.006545 \\ 0.031517 \\ 0.011286 \\ 0.054588 \\ 0.049306 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0.0022 \\ 0.0022 \\ 0.002328 \\ 0.002328 \\ 0 \\ 0.000386 \\ 0.000386 \\ 0.002813 \\ 0.002813 \\ 0.002613 \\ 0.002613 \\ 0.000007 \\ 0.000007 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0.00817 \\ 0.007379 \\ 0.008171 \\ 0.008636 \\ 0 \\ 0.014825 \\ 0.000241 \\ 0.006332 \\ 0.006453 \\ 0.010341 \\ 0.003863 \\ 0.022044 \\ 0.014791 \\ 0 \end{pmatrix} $ π
Qubit 0 ---|Gxpi2|-|Gxpi2|-|Gypi2|--- Qubit 1 ---| |-| |-| |--- $ \begin{pmatrix} 1 \\ 0.991701 \\ 0.988421e^{i0.992\pi} \\ 0.988421e^{-i0.992\pi} \\ 0.986273 \\ 0.982149e^{i0.992\pi} \\ 0.982149e^{-i0.992\pi} \\ 0.98101 \\ 0.974075e^{i0.031\pi} \\ 0.974075e^{-i0.031\pi} \\ 0.970885e^{i0.961\pi} \\ 0.970885e^{-i0.961\pi} \\ 0.970547e^{i0.976\pi} \\ 0.970547e^{-i0.976\pi} \\ 0.970417e^{i0.033\pi} \\ 0.970417e^{-i0.033\pi} \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.013675 \\ 0.031312e^{i0.321\pi} \\ 0.031312e^{i0.321\pi} \\ 0.015026 \\ 0.035396e^{i0.317\pi} \\ 0.035396e^{i0.317\pi} \\ 0.023035 \\ 0.058434e^{i0.359\pi} \\ 0.058434e^{i0.359\pi} \\ 0.112596e^{i0.149\pi} \\ 0.112596e^{i0.149\pi} \\ 0.077277e^{i0.142\pi} \\ 0.077277e^{i0.142\pi} \\ 0.061884e^{i0.287\pi} \\ 0.061884e^{i0.287\pi} \end{pmatrix} $ $ \begin{pmatrix} 1 \\ 0.990018 \\ 0.988425e^{i0.997\pi} \\ 0.988425e^{-i0.997\pi} \\ 0.986591 \\ 0.983148e^{i0.996\pi} \\ 0.983148e^{-i0.996\pi} \\ 0.982082 \\ 0.973274e^{i0.031\pi} \\ 0.973274e^{-i0.031\pi} \\ 0.971802e^{i0.965\pi} \\ 0.971802e^{-i0.965\pi} \\ 0.96913e^{i0.972\pi} \\ 0.96913e^{-i0.972\pi} \\ 0.970865e^{i0.032\pi} \\ 0.970865e^{-i0.032\pi} \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.001683 \\ 0.01304 \\ 0.01304 \\ 0.000318 \\ 0.01068 \\ 0.01068 \\ 0.001072 \\ 0.002149 \\ 0.002149 \\ 0.012612 \\ 0.012612 \\ 0.011952 \\ 0.011952 \\ 0.004022 \\ 0.004022 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.013675 \\ 0.031312 \\ 0.031312 \\ 0.015026 \\ 0.035396 \\ 0.035396 \\ 0.023035 \\ 0.058434 \\ 0.058434 \\ 0.112596 \\ 0.112596 \\ 0.077277 \\ 0.077277 \\ 0.061884 \\ 0.061884 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.018198 \\ 0.023105 \\ 0.023105 \\ 0.026952 \\ 0.034458 \\ 0.034458 \\ 0.036568 \\ 0.05196 \\ 0.05196 \\ 0.056571 \\ 0.056571 \\ 0.059484 \\ 0.059484 \\ 0.057864 \\ 0.057864 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.013539 \\ 0.016345 \\ 0.016708 \\ 0.014825 \\ 0.018669 \\ 0.019153 \\ 0.022622 \\ 0.026723 \\ 0.021905 \\ 0.086246 \\ 0.107811 \\ 0.061385 \\ 0.073244 \\ 0.040878 \\ 0.033377 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ -0.008334 \\ -0.011646 \\ -0.011646 \\ -0.013822 \\ -0.018012 \\ -0.018012 \\ -0.019173 \\ -0.026267 \\ -0.026267 \\ -0.029547 \\ -0.029547 \\ -0.029896 \\ -0.029896 \\ -0.030029 \\ -0.030029 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.013695 \\ -0.016017 \\ -0.017355 \\ 0.01512 \\ -0.018557 \\ -0.020042 \\ 0.023209 \\ 0.031658 \\ 0.02174 \\ -0.098613 \\ -0.1146 \\ -0.070638 \\ -0.076648 \\ 0.044602 \\ 0.034946 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0.992312 \\ -0.992312 \\ 0 \\ 0.992484 \\ -0.992484 \\ 0 \\ 0.030785 \\ -0.030785 \\ 0.960648 \\ -0.960648 \\ 0.975929 \\ -0.975929 \\ 0.033357 \\ -0.033357 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ -0.008794 \\ 1.991459 \\ 0 \\ -0.009959 \\ 1.990327 \\ 0 \\ 0.015867 \\ 0.017578 \\ -0.022761 \\ -0.014004 \\ -0.013551 \\ -0.009899 \\ 0.013874 \\ 0.016559 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0.001699 \\ 0.000004 \\ 0.000004 \\ 0.000322 \\ 0.001017 \\ 0.001017 \\ 0.001093 \\ 0.000823 \\ 0.000823 \\ 0.000944 \\ 0.000944 \\ 0.001461 \\ 0.001461 \\ 0.000461 \\ 0.000461 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.013695 \\ 0.016017 \\ 0.017355 \\ 0.01512 \\ 0.018557 \\ 0.020042 \\ 0.023209 \\ 0.031658 \\ 0.02174 \\ 0.098613 \\ 0.1146 \\ 0.070638 \\ 0.076648 \\ 0.044602 \\ 0.034946 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0.0042 \\ 0.0042 \\ 0 \\ 0.003444 \\ 0.003444 \\ 0 \\ 0.000652 \\ 0.000652 \\ 0.004122 \\ 0.004122 \\ 0.003895 \\ 0.003895 \\ 0.001311 \\ 0.001311 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0.008794 \\ 1.991459 \\ 0 \\ 0.009959 \\ 1.990327 \\ 0 \\ 0.015867 \\ 0.017578 \\ 0.022761 \\ 0.014004 \\ 0.013551 \\ 0.009899 \\ 0.013874 \\ 0.016559 \end{pmatrix} $ π
Qubit 0 ---| |-| |-| |--- Qubit 1 ---|Gxpi2|-|Gxpi2|-|Gypi2|--- $ \begin{pmatrix} 1 \\ 0.989569 \\ 0.989362e^{i0.998\pi} \\ 0.989362e^{-i0.998\pi} \\ 0.988521e^{i0.009\pi} \\ 0.988521e^{-i0.009\pi} \\ 0.987493 \\ 0.985434e^{i0.993\pi} \\ 0.985434e^{-i0.993\pi} \\ 0.982696e^{i0.004\pi} \\ 0.982696e^{-i0.004\pi} \\ 0.981781e^{i0.997\pi} \\ 0.981781e^{-i0.997\pi} \\ 0.980289e^{i0.994\pi} \\ 0.980289e^{-i0.994\pi} \\ 0.980011 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.036346 \\ 0.026566e^{i0.310\pi} \\ 0.026566e^{i0.310\pi} \\ 0.042282e^{i0.233\pi} \\ 0.042282e^{i0.233\pi} \\ 0.017259 \\ 0.065153e^{i0.171\pi} \\ 0.065153e^{i0.171\pi} \\ 0.045267e^{i0.408\pi} \\ 0.045267e^{i0.408\pi} \\ 0.038194e^{i0.372\pi} \\ 0.038194e^{i0.372\pi} \\ 0.105627e^{i0.286\pi} \\ 0.105627e^{i0.286\pi} \\ 0.023971 \end{pmatrix} $ $ \begin{pmatrix} 1 \\ 0.988218 \\ 0.987942e^{i0.999\pi} \\ 0.987942e^{-i0.999\pi} \\ 0.988371e^{i0.006\pi} \\ 0.988371e^{-i0.006\pi} \\ 0.986835 \\ 0.984504e^{i0.993\pi} \\ 0.984504e^{-i0.993\pi} \\ 0.981678e^{i0.007\pi} \\ 0.981678e^{-i0.007\pi} \\ -0.982095 \\ -0.984331 \\ 0.98255e^{i0.994\pi} \\ 0.98255e^{-i0.994\pi} \\ 0.981631 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.001351 \\ 0.003303 \\ 0.003303 \\ 0.008859 \\ 0.008859 \\ 0.000658 \\ 0.001943 \\ 0.001943 \\ 0.008278 \\ 0.008278 \\ 0.010084 \\ 0.010407 \\ 0.002267 \\ 0.002267 \\ 0.00162 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.036346 \\ 0.026566 \\ 0.026566 \\ 0.042282 \\ 0.042282 \\ 0.017259 \\ 0.065153 \\ 0.065153 \\ 0.045267 \\ 0.045267 \\ 0.038194 \\ 0.038194 \\ 0.105627 \\ 0.105627 \\ 0.023971 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.022089 \\ 0.022572 \\ 0.022572 \\ 0.023013 \\ 0.023013 \\ 0.025508 \\ 0.029838 \\ 0.029838 \\ 0.035342 \\ 0.035342 \\ 0.035849 \\ 0.033654 \\ 0.036817 \\ 0.036817 \\ 0.037991 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.035918 \\ 0.014712 \\ 0.014768 \\ 0.031676 \\ 0.030446 \\ 0.017032 \\ 0.053886 \\ 0.05628 \\ 0.012931 \\ 0.012398 \\ 0.014641 \\ 0.014674 \\ 0.063369 \\ 0.065958 \\ 0.023531 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ -0.010485 \\ -0.010695 \\ -0.010695 \\ -0.011545 \\ -0.011545 \\ -0.012586 \\ -0.014673 \\ -0.014673 \\ -0.017455 \\ -0.017455 \\ -0.018387 \\ -0.018387 \\ -0.019907 \\ -0.019907 \\ -0.020192 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.036071 \\ -0.014828 \\ -0.015053 \\ 0.032446 \\ 0.030902 \\ 0.017327 \\ -0.056914 \\ -0.058698 \\ 0.014538 \\ 0.013447 \\ -0.014261 \\ -0.015018 \\ -0.063529 \\ -0.06734 \\ 0.024166 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0.99844 \\ -0.99844 \\ 0.009153 \\ -0.009153 \\ 0 \\ 0.992531 \\ -0.992531 \\ 0.004044 \\ -0.004044 \\ 0.996733 \\ -0.996733 \\ 0.993685 \\ -0.993685 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ -0.007202 \\ 1.992844 \\ 0.008531 \\ 0.009109 \\ 0 \\ -0.011856 \\ 1.989023 \\ 0.013802 \\ 0.013922 \\ -0.011617 \\ 1.988475 \\ -0.02907 \\ 1.97173 \\ 0 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0.001366 \\ 0.001437 \\ 0.001437 \\ 0.000152 \\ 0.000152 \\ 0.000667 \\ 0.000944 \\ 0.000944 \\ 0.001037 \\ 0.001037 \\ 0.00032 \\ 0.002594 \\ 0.002303 \\ 0.002303 \\ 0.001652 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.036071 \\ 0.014828 \\ 0.015053 \\ 0.032446 \\ 0.030902 \\ 0.017327 \\ 0.056914 \\ 0.058698 \\ 0.014538 \\ 0.013447 \\ 0.014261 \\ 0.015018 \\ 0.063529 \\ 0.06734 \\ 0.024166 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0.00096 \\ 0.00096 \\ 0.002853 \\ 0.002853 \\ 0 \\ 0.000551 \\ 0.000551 \\ 0.002663 \\ 0.002663 \\ 0.003267 \\ 1.996733 \\ 0.000056 \\ 0.000056 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0.007202 \\ 1.992844 \\ 0.008531 \\ 0.009109 \\ 0 \\ 0.011856 \\ 1.989023 \\ 0.013802 \\ 0.013922 \\ 0.011617 \\ 1.988475 \\ 0.02907 \\ 1.97173 \\ 0 \end{pmatrix} $ π
Qubit 0 ---| |-| |-|C1|--- Qubit 1 ---|Gxpi2|-|Gypi2|-|C0|--- $ \begin{pmatrix} 1 \\ 0.980029e^{i0.000\pi} \\ 0.980029e^{-i0.000\pi} \\ 0.970739e^{i0.661\pi} \\ 0.970739e^{-i0.661\pi} \\ 0.965594e^{i0.850\pi} \\ 0.965594e^{-i0.850\pi} \\ 0.96355e^{i0.153\pi} \\ 0.96355e^{-i0.153\pi} \\ 0.962948e^{i0.492\pi} \\ 0.962948e^{-i0.492\pi} \\ 0.960081e^{i0.644\pi} \\ 0.960081e^{-i0.644\pi} \\ 0.959069 \\ 0.958535e^{i0.505\pi} \\ 0.958535e^{-i0.505\pi} \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.059365e^{i0.442\pi} \\ 0.059365e^{i0.442\pi} \\ 0.023564e^{i0.315\pi} \\ 0.023564e^{i0.315\pi} \\ 0.06433e^{i0.244\pi} \\ 0.06433e^{i0.244\pi} \\ 0.086548e^{i0.279\pi} \\ 0.086548e^{i0.279\pi} \\ 0.0664e^{i0.180\pi} \\ 0.0664e^{i0.180\pi} \\ 0.032125e^{i0.242\pi} \\ 0.032125e^{i0.242\pi} \\ 0.029432 \\ 0.041859e^{i0.233\pi} \\ 0.041859e^{i0.233\pi} \end{pmatrix} $ $ \begin{pmatrix} 1 \\ 0.975902 \\ 0.982908 \\ 0.971652e^{i0.660\pi} \\ 0.971652e^{-i0.660\pi} \\ 0.966004e^{i0.846\pi} \\ 0.966004e^{-i0.846\pi} \\ 0.964439e^{i0.158\pi} \\ 0.964439e^{-i0.158\pi} \\ 0.964237e^{i0.497\pi} \\ 0.964237e^{-i0.497\pi} \\ 0.959907e^{i0.653\pi} \\ 0.959907e^{-i0.653\pi} \\ 0.957884 \\ 0.956447e^{i0.501\pi} \\ 0.956447e^{-i0.501\pi} \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.004325 \\ 0.003159 \\ 0.002446 \\ 0.002446 \\ 0.013589 \\ 0.013589 \\ 0.014908 \\ 0.014908 \\ 0.014689 \\ 0.014689 \\ 0.02662 \\ 0.02662 \\ 0.001185 \\ 0.012833 \\ 0.012833 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.059365 \\ 0.059365 \\ 0.023564 \\ 0.023564 \\ 0.06433 \\ 0.06433 \\ 0.086548 \\ 0.086548 \\ 0.0664 \\ 0.0664 \\ 0.032125 \\ 0.032125 \\ 0.029432 \\ 0.041859 \\ 0.041859 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.043589 \\ 0.036723 \\ 0.056781 \\ 0.056781 \\ 0.067324 \\ 0.067324 \\ 0.070825 \\ 0.070825 \\ 0.071597 \\ 0.071597 \\ 0.078766 \\ 0.078766 \\ 0.081323 \\ 0.083292 \\ 0.083292 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.010528 \\ 0.010604 \\ 0.004964 \\ 0.017108 \\ 0.018819 \\ 0.060539 \\ 0.072396 \\ 0.021456 \\ 0.054585 \\ 0.053437 \\ 0.009521 \\ 0.030168 \\ 0.028193 \\ 0.029765 \\ 0.029865 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ -0.020174 \\ -0.020174 \\ -0.029697 \\ -0.029697 \\ -0.035011 \\ -0.035011 \\ -0.037131 \\ -0.037131 \\ -0.037755 \\ -0.037755 \\ -0.040737 \\ -0.040737 \\ -0.041792 \\ -0.042349 \\ -0.042349 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.012758 \\ 0.012604 \\ 0.011435 \\ -0.024497 \\ -0.020136 \\ -0.065651 \\ 0.08016 \\ 0.022442 \\ 0.039303 \\ -0.03428 \\ 0.010566 \\ -0.031746 \\ 0.030227 \\ 0.028766 \\ -0.029528 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.000422 \\ -0.000422 \\ 0.660847 \\ -0.660847 \\ 0.85041 \\ -0.85041 \\ 0.153375 \\ -0.153375 \\ 0.491783 \\ -0.491783 \\ 0.643858 \\ -0.643858 \\ 0 \\ 0.504748 \\ -0.504748 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0.018726 \\ 0.018738 \\ -0.006766 \\ 0.000611 \\ -0.020443 \\ -0.006586 \\ 0.010154 \\ 0.027363 \\ -0.017514 \\ 0.019483 \\ -0.010047 \\ 0.00387 \\ 0 \\ -0.010193 \\ 0.01052 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0.00422 \\ 0.002934 \\ 0.00094 \\ 0.00094 \\ 0.000424 \\ 0.000424 \\ 0.000923 \\ 0.000923 \\ 0.001337 \\ 0.001337 \\ 0.000182 \\ 0.000182 \\ 0.001237 \\ 0.002181 \\ 0.002181 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.012758 \\ 0.012604 \\ 0.011435 \\ 0.024497 \\ 0.020136 \\ 0.065651 \\ 0.08016 \\ 0.022442 \\ 0.039303 \\ 0.03428 \\ 0.010566 \\ 0.031746 \\ 0.030227 \\ 0.028766 \\ 0.029528 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.000422 \\ 0.000422 \\ 0.000744 \\ 0.000744 \\ 0.004477 \\ 0.004477 \\ 0.004914 \\ 0.004914 \\ 0.004834 \\ 0.004834 \\ 0.008827 \\ 0.008827 \\ 0 \\ 0.00421 \\ 0.00421 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0.018726 \\ 0.018738 \\ 0.006766 \\ 0.000611 \\ 0.020443 \\ 0.006586 \\ 0.010154 \\ 0.027363 \\ 0.017514 \\ 0.019483 \\ 0.010047 \\ 0.00387 \\ 0 \\ 0.010193 \\ 0.01052 \end{pmatrix} $ π
Qubit 0 ---|C1|-| |-|Gxpi2|-|Gxpi2|--- Qubit 1 ---|C0|-|Gxpi2|-| |-| |--- $ \begin{pmatrix} 1 \\ -0.976304 \\ -0.964205 \\ 0.963423e^{i0.490\pi} \\ 0.963423e^{-i0.490\pi} \\ 0.961888e^{i0.508\pi} \\ 0.961888e^{-i0.508\pi} \\ 0.961633 \\ 0.958608e^{i0.996\pi} \\ 0.958608e^{-i0.996\pi} \\ 0.958365e^{i0.515\pi} \\ 0.958365e^{-i0.515\pi} \\ 0.958313e^{i0.486\pi} \\ 0.958313e^{-i0.486\pi} \\ 0.952865e^{i0.002\pi} \\ 0.952865e^{-i0.002\pi} \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.044964 \\ 0.199082 \\ 0.055404e^{i0.217\pi} \\ 0.055404e^{i0.217\pi} \\ 0.069971e^{i0.377\pi} \\ 0.069971e^{i0.377\pi} \\ 0.06657 \\ 0.066479e^{i0.093\pi} \\ 0.066479e^{i0.093\pi} \\ 0.049845e^{i0.203\pi} \\ 0.049845e^{i0.203\pi} \\ 0.081144e^{i0.243\pi} \\ 0.081144e^{i0.243\pi} \\ 0.07755e^{i0.249\pi} \\ 0.07755e^{i0.249\pi} \end{pmatrix} $ $ \begin{pmatrix} 1 \\ -0.981494 \\ -0.959108 \\ 0.958809e^{i0.488\pi} \\ 0.958809e^{-i0.488\pi} \\ 0.96412e^{i0.512\pi} \\ 0.96412e^{-i0.512\pi} \\ 0.954803 \\ 0.957082e^{i0.998\pi} \\ 0.957082e^{-i0.998\pi} \\ 0.957597e^{i0.513\pi} \\ 0.957597e^{-i0.513\pi} \\ 0.963278e^{i0.486\pi} \\ 0.963278e^{-i0.486\pi} \\ 0.95599e^{i0.002\pi} \\ 0.95599e^{-i0.002\pi} \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.00519 \\ 0.005097 \\ 0.007459 \\ 0.007459 \\ 0.011764 \\ 0.011764 \\ 0.00683 \\ 0.007179 \\ 0.007179 \\ 0.004728 \\ 0.004728 \\ 0.005371 \\ 0.005371 \\ 0.003334 \\ 0.003334 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.044964 \\ 0.199082 \\ 0.055404 \\ 0.055404 \\ 0.069971 \\ 0.069971 \\ 0.06657 \\ 0.066479 \\ 0.066479 \\ 0.049845 \\ 0.049845 \\ 0.081144 \\ 0.081144 \\ 0.07755 \\ 0.07755 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.041764 \\ 0.075223 \\ 0.076279 \\ 0.076279 \\ 0.072692 \\ 0.072692 \\ 0.081829 \\ 0.082558 \\ 0.082558 \\ 0.082283 \\ 0.082283 \\ 0.07688 \\ 0.07688 \\ 0.089071 \\ 0.089071 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.044132 \\ 0.190941 \\ 0.042716 \\ 0.039719 \\ 0.024503 \\ 0.026476 \\ 0.063561 \\ 0.060574 \\ 0.061336 \\ 0.036703 \\ 0.039908 \\ 0.059008 \\ 0.053938 \\ 0.052847 \\ 0.052263 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ -0.023981 \\ -0.036451 \\ -0.037263 \\ -0.037263 \\ -0.038857 \\ -0.038857 \\ -0.039122 \\ -0.042273 \\ -0.042273 \\ -0.042527 \\ -0.042527 \\ -0.042581 \\ -0.042581 \\ -0.048282 \\ -0.048282 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ -0.04715 \\ -0.231267 \\ 0.037767 \\ -0.034377 \\ 0.064839 \\ -0.070099 \\ 0.066935 \\ -0.068207 \\ -0.068826 \\ 0.029465 \\ -0.032583 \\ 0.060777 \\ -0.055157 \\ 0.057907 \\ 0.057214 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 1 \\ 1 \\ 0.49037 \\ -0.49037 \\ 0.508491 \\ -0.508491 \\ 0 \\ 0.995678 \\ -0.995678 \\ 0.51486 \\ -0.51486 \\ 0.4864 \\ -0.4864 \\ 0.002156 \\ -0.002156 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ -0.013347 \\ 0.01507 \\ -0.00874 \\ 0.008776 \\ 0 \\ -0.007081 \\ 1.99353 \\ -0.013348 \\ 0.013252 \\ -0.017587 \\ 0.021435 \\ 0.017134 \\ 0.017381 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0.005302 \\ 0.0053 \\ 0.004801 \\ 0.004801 \\ 0.002318 \\ 0.002318 \\ 0.007128 \\ 0.001593 \\ 0.001593 \\ 0.000802 \\ 0.000802 \\ 0.005168 \\ 0.005168 \\ 0.003274 \\ 0.003274 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.04715 \\ 0.231267 \\ 0.037767 \\ 0.034377 \\ 0.064839 \\ 0.070099 \\ 0.066935 \\ 0.068207 \\ 0.068826 \\ 0.029465 \\ 0.032583 \\ 0.060777 \\ 0.055157 \\ 0.057907 \\ 0.057214 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0.001941 \\ 0.001941 \\ 0.003818 \\ 0.003818 \\ 0 \\ 0.002331 \\ 0.002331 \\ 0.00155 \\ 0.00155 \\ 0.000678 \\ 0.000678 \\ 0.000387 \\ 0.000387 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0.013347 \\ 0.01507 \\ 0.00874 \\ 0.008776 \\ 0 \\ 0.007081 \\ 1.99353 \\ 0.013348 \\ 0.013252 \\ 0.017587 \\ 0.021435 \\ 0.017134 \\ 0.017381 \end{pmatrix} $ π
Qubit 0 ---|Gxpi2|-| |-| |-|Gxpi2|-| |-|Gypi2|--- Qubit 1 ---| |-|Gxpi2|-|Gypi2|-| |-|Gypi2|-| |--- $ \begin{pmatrix} 1 \\ 0.968218 \\ 0.965454e^{i0.994\pi} \\ 0.965454e^{-i0.994\pi} \\ 0.964372e^{i0.982\pi} \\ 0.964372e^{-i0.982\pi} \\ 0.961231e^{i0.989\pi} \\ 0.961231e^{-i0.989\pi} \\ 0.961069e^{i0.004\pi} \\ 0.961069e^{-i0.004\pi} \\ 0.960184e^{i0.030\pi} \\ 0.960184e^{-i0.030\pi} \\ 0.958621e^{i0.976\pi} \\ 0.958621e^{-i0.976\pi} \\ 0.953279e^{i0.001\pi} \\ 0.953279e^{-i0.001\pi} \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.04074 \\ 0.083948e^{i0.267\pi} \\ 0.083948e^{i0.267\pi} \\ 0.083218e^{i0.210\pi} \\ 0.083218e^{i0.210\pi} \\ 0.082867e^{i0.286\pi} \\ 0.082867e^{i0.286\pi} \\ 0.099533e^{i0.246\pi} \\ 0.099533e^{i0.246\pi} \\ 0.098065e^{i0.404\pi} \\ 0.098065e^{i0.404\pi} \\ 0.075274e^{i0.166\pi} \\ 0.075274e^{i0.166\pi} \\ 0.067802e^{i0.141\pi} \\ 0.067802e^{i0.141\pi} \end{pmatrix} $ $ \begin{pmatrix} 1 \\ 0.972876 \\ 0.974809e^{i0.990\pi} \\ 0.974809e^{-i0.990\pi} \\ 0.964248e^{i0.986\pi} \\ 0.964248e^{-i0.986\pi} \\ 0.956997e^{i0.990\pi} \\ 0.956997e^{-i0.990\pi} \\ 0.953006e^{i0.005\pi} \\ 0.953006e^{-i0.005\pi} \\ 0.95882e^{i0.024\pi} \\ 0.95882e^{-i0.024\pi} \\ 0.954763e^{i0.985\pi} \\ 0.954763e^{-i0.985\pi} \\ 0.95486 \\ 0.963923 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.004658 \\ 0.016268 \\ 0.016268 \\ 0.012038 \\ 0.012038 \\ 0.006274 \\ 0.006274 \\ 0.008435 \\ 0.008435 \\ 0.016693 \\ 0.016693 \\ 0.026175 \\ 0.026175 \\ 0.002316 \\ 0.010778 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.04074 \\ 0.083948 \\ 0.083948 \\ 0.083218 \\ 0.083218 \\ 0.082867 \\ 0.082867 \\ 0.099533 \\ 0.099533 \\ 0.098065 \\ 0.098065 \\ 0.075274 \\ 0.075274 \\ 0.067802 \\ 0.067802 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.058044 \\ 0.058955 \\ 0.058955 \\ 0.070179 \\ 0.070179 \\ 0.080116 \\ 0.080116 \\ 0.084098 \\ 0.084098 \\ 0.079494 \\ 0.079494 \\ 0.085079 \\ 0.085079 \\ 0.089753 \\ 0.081114 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.039634 \\ 0.052853 \\ 0.056387 \\ 0.060506 \\ 0.066031 \\ 0.047809 \\ 0.050819 \\ 0.068937 \\ 0.066796 \\ 0.030023 \\ 0.025755 \\ 0.059258 \\ 0.065241 \\ 0.058468 \\ 0.059023 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ -0.032298 \\ -0.035156 \\ -0.035156 \\ -0.036278 \\ -0.036278 \\ -0.039541 \\ -0.039541 \\ -0.039709 \\ -0.039709 \\ -0.04063 \\ -0.04063 \\ -0.04226 \\ -0.04226 \\ -0.047847 \\ -0.047847 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.041216 \\ -0.056104 \\ -0.058809 \\ -0.065397 \\ -0.072218 \\ -0.049909 \\ -0.055206 \\ 0.07457 \\ 0.072924 \\ 0.042711 \\ 0.02567 \\ -0.066062 \\ -0.072803 \\ 0.062714 \\ 0.062618 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0.994071 \\ -0.994071 \\ 0.982138 \\ -0.982138 \\ 0.988753 \\ -0.988753 \\ 0.004196 \\ -0.004196 \\ 0.029828 \\ -0.029828 \\ 0.976101 \\ -0.976101 \\ 0.000565 \\ -0.000565 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ -0.022169 \\ 1.978503 \\ -0.01929 \\ -0.016804 \\ -0.023224 \\ 1.97793 \\ 0.021098 \\ 0.021713 \\ 0.028782 \\ 0.03105 \\ -0.015003 \\ -0.011605 \\ 0.009098 \\ 0.009167 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0.004799 \\ 0.009642 \\ 0.009642 \\ 0.000128 \\ 0.000128 \\ 0.004414 \\ 0.004414 \\ 0.008425 \\ 0.008425 \\ 0.001422 \\ 0.001422 \\ 0.004032 \\ 0.004032 \\ 0.001657 \\ 0.011103 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.041216 \\ 0.056104 \\ 0.058809 \\ 0.065397 \\ 0.072218 \\ 0.049909 \\ 0.055206 \\ 0.07457 \\ 0.072924 \\ 0.042711 \\ 0.02567 \\ 0.066062 \\ 0.072803 \\ 0.062714 \\ 0.062618 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0.004367 \\ 0.004367 \\ 0.003974 \\ 0.003974 \\ 0.001537 \\ 0.001537 \\ 0.000824 \\ 0.000824 \\ 0.005519 \\ 0.005519 \\ 0.008614 \\ 0.008614 \\ 0.000565 \\ 0.000565 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0.022169 \\ 1.978503 \\ 0.01929 \\ 0.016804 \\ 0.023224 \\ 1.97793 \\ 0.021098 \\ 0.021713 \\ 0.028782 \\ 0.03105 \\ 0.015003 \\ 0.011605 \\ 0.009098 \\ 0.009167 \end{pmatrix} $ π
Qubit 0 ---|Gxpi2|-| |-| |-|Gypi2|-| |-| |--- Qubit 1 ---| |-|Gypi2|-|Gxpi2|-| |-|Gxpi2|-|Gxpi2|--- $ \begin{pmatrix} 1 \\ 0.973449e^{i0.676\pi} \\ 0.973449e^{-i0.676\pi} \\ 0.972712 \\ 0.968836e^{i0.007\pi} \\ 0.968836e^{-i0.007\pi} \\ 0.965701e^{i0.670\pi} \\ 0.965701e^{-i0.670\pi} \\ 0.965045 \\ 0.962978e^{i0.675\pi} \\ 0.962978e^{-i0.675\pi} \\ 0.962348e^{i0.669\pi} \\ 0.962348e^{-i0.669\pi} \\ 0.957771 \\ 0.954802e^{i0.655\pi} \\ 0.954802e^{-i0.655\pi} \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.053575e^{i0.223\pi} \\ 0.053575e^{i0.223\pi} \\ 0.05266 \\ 0.035119e^{i0.333\pi} \\ 0.035119e^{i0.333\pi} \\ 0.076826e^{i0.309\pi} \\ 0.076826e^{i0.309\pi} \\ 0.034133 \\ 0.096933e^{i0.245\pi} \\ 0.096933e^{i0.245\pi} \\ 0.130691e^{i0.219\pi} \\ 0.130691e^{i0.219\pi} \\ 0.100893 \\ 0.105384e^{i0.208\pi} \\ 0.105384e^{i0.208\pi} \end{pmatrix} $ $ \begin{pmatrix} 1 \\ 0.975831e^{i0.672\pi} \\ 0.975831e^{-i0.672\pi} \\ 0.974564 \\ 0.96733e^{i0.002\pi} \\ 0.96733e^{-i0.002\pi} \\ 0.966254e^{i0.671\pi} \\ 0.966254e^{-i0.671\pi} \\ 0.965865 \\ 0.95876e^{i0.672\pi} \\ 0.95876e^{-i0.672\pi} \\ 0.963091e^{i0.669\pi} \\ 0.963091e^{-i0.669\pi} \\ 0.957152 \\ 0.955857e^{i0.658\pi} \\ 0.955857e^{-i0.658\pi} \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.013768 \\ 0.013768 \\ 0.001852 \\ 0.013821 \\ 0.013821 \\ 0.002812 \\ 0.002812 \\ 0.000821 \\ 0.011291 \\ 0.011291 \\ 0.000944 \\ 0.000944 \\ 0.000619 \\ 0.01033 \\ 0.01033 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.053575 \\ 0.053575 \\ 0.05266 \\ 0.035119 \\ 0.035119 \\ 0.076826 \\ 0.076826 \\ 0.034133 \\ 0.096933 \\ 0.096933 \\ 0.130691 \\ 0.130691 \\ 0.100893 \\ 0.105384 \\ 0.105384 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.05017 \\ 0.05017 \\ 0.05203 \\ 0.06291 \\ 0.06291 \\ 0.066892 \\ 0.066892 \\ 0.067897 \\ 0.07679 \\ 0.07679 \\ 0.073172 \\ 0.073172 \\ 0.083267 \\ 0.087398 \\ 0.087398 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.013772 \\ 0.054803 \\ 0.05132 \\ 0.017118 \\ 0.016853 \\ 0.014597 \\ 0.057565 \\ 0.032968 \\ 0.023011 \\ 0.091504 \\ 0.034491 \\ 0.133131 \\ 0.09657 \\ 0.032182 \\ 0.108547 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ -0.02691 \\ -0.02691 \\ -0.027668 \\ -0.031659 \\ -0.031659 \\ -0.034901 \\ -0.034901 \\ -0.035581 \\ -0.037725 \\ -0.037725 \\ -0.038379 \\ -0.038379 \\ -0.043146 \\ -0.046251 \\ -0.046251 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.009527 \\ -0.053551 \\ 0.052723 \\ 0.019098 \\ 0.017768 \\ 0.035429 \\ -0.082687 \\ 0.034758 \\ 0.026337 \\ -0.102214 \\ 0.029509 \\ -0.134951 \\ 0.100154 \\ 0.023734 \\ -0.104292 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.676059 \\ -0.676059 \\ 0 \\ 0.006996 \\ -0.006996 \\ 0.670042 \\ -0.670042 \\ 0 \\ 0.675049 \\ -0.675049 \\ 0.669116 \\ -0.669116 \\ 0 \\ 0.654831 \\ -0.654831 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ -0.017172 \\ 0.005758 \\ 0 \\ 0.009678 \\ 0.00994 \\ -0.02218 \\ 0.001843 \\ 0 \\ -0.030502 \\ 0.00881 \\ -0.041575 \\ 0.017049 \\ 0 \\ -0.033902 \\ 0.01634 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0.002444 \\ 0.002444 \\ 0.001903 \\ 0.001556 \\ 0.001556 \\ 0.000572 \\ 0.000572 \\ 0.00085 \\ 0.004389 \\ 0.004389 \\ 0.000772 \\ 0.000772 \\ 0.000647 \\ 0.001104 \\ 0.001104 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.009527 \\ 0.053551 \\ 0.052723 \\ 0.019098 \\ 0.017768 \\ 0.035429 \\ 0.082687 \\ 0.034758 \\ 0.026337 \\ 0.102214 \\ 0.029509 \\ 0.134951 \\ 0.100154 \\ 0.023734 \\ 0.104292 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.004429 \\ 0.004429 \\ 0 \\ 0.004517 \\ 0.004517 \\ 0.000909 \\ 0.000909 \\ 0 \\ 0.00347 \\ 0.00347 \\ 0.000192 \\ 0.000192 \\ 0 \\ 0.003424 \\ 0.003424 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0.017172 \\ 0.005758 \\ 0 \\ 0.009678 \\ 0.00994 \\ 0.02218 \\ 0.001843 \\ 0 \\ 0.030502 \\ 0.00881 \\ 0.041575 \\ 0.017049 \\ 0 \\ 0.033902 \\ 0.01634 \end{pmatrix} $ π
Qubit 0 ---|C1|-| |-|Gypi2|-|C1|-| |-|Gxpi2|--- Qubit 1 ---|C0|-|Gxpi2|-| |-|C0|-|Gypi2|-| |--- $ \begin{pmatrix} 1 \\ 0.941908 \\ 0.934951e^{i0.997\pi} \\ 0.934951e^{-i0.997\pi} \\ 0.934088 \\ 0.933979e^{i0.983\pi} \\ 0.933979e^{-i0.983\pi} \\ 0.928567e^{i0.023\pi} \\ 0.928567e^{-i0.023\pi} \\ 0.92721e^{i0.984\pi} \\ 0.92721e^{-i0.984\pi} \\ 0.91776e^{i0.013\pi} \\ 0.91776e^{-i0.013\pi} \\ 0.917178e^{i0.990\pi} \\ 0.917178e^{-i0.990\pi} \\ 0.911384 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.041915 \\ 0.089722e^{i0.270\pi} \\ 0.089722e^{i0.270\pi} \\ 0.118509 \\ 0.129413e^{i0.240\pi} \\ 0.129413e^{i0.240\pi} \\ 0.076064e^{i0.171\pi} \\ 0.076064e^{i0.171\pi} \\ 0.15804e^{i0.253\pi} \\ 0.15804e^{i0.253\pi} \\ 0.088432e^{i0.171\pi} \\ 0.088432e^{i0.171\pi} \\ 0.07926e^{i0.192\pi} \\ 0.07926e^{i0.192\pi} \\ 0.061055 \end{pmatrix} $ $ \begin{pmatrix} 1 \\ 0.939091 \\ -0.936983 \\ -0.928601 \\ 0.924899e^{i0.001\pi} \\ 0.940472e^{i0.995\pi} \\ 0.940472e^{-i0.995\pi} \\ 0.932991e^{i0.005\pi} \\ 0.932991e^{-i0.005\pi} \\ 0.928191e^{i0.996\pi} \\ 0.928191e^{-i0.996\pi} \\ 0.912877e^{i0.005\pi} \\ 0.912877e^{-i0.005\pi} \\ 0.911691e^{i0.994\pi} \\ 0.911691e^{-i0.994\pi} \\ 0.924899e^{-i0.001\pi} \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.002817 \\ 0.010106 \\ 0.011723 \\ 0.00958 \\ 0.034884 \\ 0.034884 \\ 0.053449 \\ 0.053449 \\ 0.03405 \\ 0.03405 \\ 0.02385 \\ 0.02385 \\ 0.01201 \\ 0.01201 \\ 0.013778 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.041915 \\ 0.089722 \\ 0.089722 \\ 0.118509 \\ 0.129413 \\ 0.129413 \\ 0.076064 \\ 0.076064 \\ 0.15804 \\ 0.15804 \\ 0.088432 \\ 0.088432 \\ 0.07926 \\ 0.07926 \\ 0.061055 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.115463 \\ 0.124016 \\ 0.131852 \\ 0.136067 \\ 0.122206 \\ 0.122206 \\ 0.135074 \\ 0.135074 \\ 0.139951 \\ 0.139951 \\ 0.162471 \\ 0.162471 \\ 0.163874 \\ 0.163874 \\ 0.157065 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.039362 \\ 0.055643 \\ 0.055145 \\ 0.109928 \\ 0.087118 \\ 0.09018 \\ 0.061918 \\ 0.05998 \\ 0.10146 \\ 0.104187 \\ 0.070469 \\ 0.068247 \\ 0.058367 \\ 0.06054 \\ 0.056305 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ -0.059848 \\ -0.067262 \\ -0.067262 \\ -0.068185 \\ -0.068301 \\ -0.068301 \\ -0.074112 \\ -0.074112 \\ -0.075575 \\ -0.075575 \\ -0.08582 \\ -0.08582 \\ -0.086453 \\ -0.086453 \\ -0.09279 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.043538 \\ -0.061816 \\ -0.063541 \\ 0.119445 \\ -0.094473 \\ -0.106969 \\ 0.071264 \\ 0.06592 \\ -0.11 \\ -0.125359 \\ 0.08226 \\ 0.078777 \\ -0.070639 \\ -0.074038 \\ 0.064844 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0.996633 \\ -0.996633 \\ 0 \\ 0.982861 \\ -0.982861 \\ 0.023279 \\ -0.023279 \\ 0.984101 \\ -0.984101 \\ 0.013216 \\ -0.013216 \\ 0.990465 \\ -0.990465 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ -0.024609 \\ 1.975806 \\ 0 \\ -0.035133 \\ 1.968294 \\ 0.010879 \\ 0.014004 \\ -0.045411 \\ 1.958228 \\ 0.013434 \\ 0.015505 \\ -0.017502 \\ 1.9839 \\ 0 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0.002995 \\ 0.002172 \\ 0.006814 \\ 0.009885 \\ 0.006927 \\ 0.006927 \\ 0.004752 \\ 0.004752 \\ 0.001058 \\ 0.001058 \\ 0.005335 \\ 0.005335 \\ 0.006001 \\ 0.006001 \\ 0.01472 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.043538 \\ 0.061816 \\ 0.063541 \\ 0.119445 \\ 0.094473 \\ 0.106969 \\ 0.071264 \\ 0.06592 \\ 0.11 \\ 0.125359 \\ 0.08226 \\ 0.078777 \\ 0.070639 \\ 0.074038 \\ 0.064844 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0.003367 \\ 1.996633 \\ 0.000929 \\ 0.011642 \\ 0.011642 \\ 0.018219 \\ 0.018219 \\ 0.011679 \\ 0.011679 \\ 0.008119 \\ 0.008119 \\ 0.003719 \\ 0.003719 \\ 0.000929 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0.024609 \\ 1.975806 \\ 0 \\ 0.035133 \\ 1.968294 \\ 0.010879 \\ 0.014004 \\ 0.045411 \\ 1.958228 \\ 0.013434 \\ 0.015505 \\ 0.017502 \\ 1.9839 \\ 0 \end{pmatrix} $ π
Qubit 0 ---|Gypi2|-|Gxpi2|-| |-|Gxpi2|-| |-|Gxpi2|-|Gypi2|-| |--- Qubit 1 ---| |-| |-|Gypi2|-| |-|Gxpi2|-| |-| |-|Gypi2|--- $ \begin{pmatrix} 1 \\ 0.969632 \\ 0.966787e^{i0.995\pi} \\ 0.966787e^{-i0.995\pi} \\ 0.946012e^{i0.006\pi} \\ 0.946012e^{-i0.006\pi} \\ 0.944607e^{i0.988\pi} \\ 0.944607e^{-i0.988\pi} \\ 0.944118 \\ 0.942092e^{i0.992\pi} \\ 0.942092e^{-i0.992\pi} \\ 0.93863 \\ 0.936176e^{i0.996\pi} \\ 0.936176e^{-i0.996\pi} \\ 0.930313e^{i0.014\pi} \\ 0.930313e^{-i0.014\pi} \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.032186 \\ 0.031875e^{i0.267\pi} \\ 0.031875e^{i0.267\pi} \\ 0.112308e^{i0.124\pi} \\ 0.112308e^{i0.124\pi} \\ 0.075543e^{i0.193\pi} \\ 0.075543e^{i0.193\pi} \\ 0.088742 \\ 0.116515e^{i0.213\pi} \\ 0.116515e^{i0.213\pi} \\ 0.133314 \\ 0.157104e^{i0.263\pi} \\ 0.157104e^{i0.263\pi} \\ 0.103492e^{i0.219\pi} \\ 0.103492e^{i0.219\pi} \end{pmatrix} $ $ \begin{pmatrix} 1 \\ 0.967227 \\ -0.965275 \\ -0.969322 \\ 0.940756e^{i0.011\pi} \\ 0.940756e^{-i0.011\pi} \\ 0.948274e^{i0.988\pi} \\ 0.948274e^{-i0.988\pi} \\ 0.946884 \\ 0.938569e^{i0.989\pi} \\ 0.938569e^{-i0.989\pi} \\ 0.93643 \\ 0.936998e^{i1.000\pi} \\ 0.936998e^{-i1.000\pi} \\ 0.93497e^{i0.011\pi} \\ 0.93497e^{-i0.011\pi} \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.002406 \\ 0.013845 \\ 0.014022 \\ 0.014346 \\ 0.014346 \\ 0.003929 \\ 0.003929 \\ 0.002766 \\ 0.007982 \\ 0.007982 \\ 0.0022 \\ 0.009569 \\ 0.009569 \\ 0.00998 \\ 0.00998 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.032186 \\ 0.031875 \\ 0.031875 \\ 0.112308 \\ 0.112308 \\ 0.075543 \\ 0.075543 \\ 0.088742 \\ 0.116515 \\ 0.116515 \\ 0.133314 \\ 0.157104 \\ 0.157104 \\ 0.103492 \\ 0.103492 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.062146 \\ 0.06688 \\ 0.062967 \\ 0.110122 \\ 0.110122 \\ 0.104255 \\ 0.104255 \\ 0.10603 \\ 0.115807 \\ 0.115807 \\ 0.121039 \\ 0.12285 \\ 0.12285 \\ 0.130225 \\ 0.130225 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.031132 \\ 0.020568 \\ 0.020654 \\ 0.101097 \\ 0.094342 \\ 0.056676 \\ 0.060969 \\ 0.084029 \\ 0.082842 \\ 0.088651 \\ 0.124839 \\ 0.099742 \\ 0.100006 \\ 0.077178 \\ 0.072188 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ -0.030838 \\ -0.033777 \\ -0.033777 \\ -0.0555 \\ -0.0555 \\ -0.056986 \\ -0.056986 \\ -0.057504 \\ -0.059652 \\ -0.059652 \\ -0.063334 \\ -0.065951 \\ -0.065951 \\ -0.072234 \\ -0.072234 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.032655 \\ -0.021605 \\ -0.022335 \\ 0.105785 \\ 0.104298 \\ -0.064755 \\ -0.068709 \\ 0.089836 \\ -0.095987 \\ -0.100887 \\ 0.132808 \\ -0.109514 \\ -0.113057 \\ 0.087015 \\ 0.0819 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0.995465 \\ -0.995465 \\ 0.006493 \\ -0.006493 \\ 0.987914 \\ -0.987914 \\ 0 \\ 0.991646 \\ -0.991646 \\ 0 \\ 0.996339 \\ -0.996339 \\ 0.013642 \\ -0.013642 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ -0.008078 \\ 1.992121 \\ 0.012239 \\ 0.013543 \\ -0.016322 \\ 1.985316 \\ 0 \\ -0.027789 \\ 1.973874 \\ 0 \\ -0.044389 \\ 1.956395 \\ 0.019541 \\ 0.021805 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0.002484 \\ 0.001565 \\ 0.002619 \\ 0.005571 \\ 0.005571 \\ 0.003874 \\ 0.003874 \\ 0.002925 \\ 0.003747 \\ 0.003747 \\ 0.002347 \\ 0.000877 \\ 0.000877 \\ 0.004993 \\ 0.004993 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.032655 \\ 0.021605 \\ 0.022335 \\ 0.105785 \\ 0.104298 \\ 0.064755 \\ 0.068709 \\ 0.089836 \\ 0.095987 \\ 0.100887 \\ 0.132808 \\ 0.109514 \\ 0.113057 \\ 0.087015 \\ 0.0819 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0.004535 \\ 1.995465 \\ 0.004504 \\ 0.004504 \\ 0.000474 \\ 0.000474 \\ 0 \\ 0.002424 \\ 0.002424 \\ 0 \\ 0.00324 \\ 0.00324 \\ 0.003013 \\ 0.003013 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0.008078 \\ 1.992121 \\ 0.012239 \\ 0.013543 \\ 0.016322 \\ 1.985316 \\ 0 \\ 0.027789 \\ 1.973874 \\ 0 \\ 0.044389 \\ 1.956395 \\ 0.019541 \\ 0.021805 \end{pmatrix} $ π
Gate or Germ Eigenvalues ($E$) Target Evals. ($T$) $|E - T|$ $1.0 - \mathrm{Re}(\bar{T}\cdot E)$ $\mathrm{Re} \log(E)$ $\mathrm{Im} \log(E)$ $|\mathrm{Re}(\log E) - \mathrm{Re}(\log T)|$ $|\mathrm{Im}(\log E) - \mathrm{Im}(\log T)|$
[]$ \begin{pmatrix} 1 \\ 0.998714e^{i0.000\pi} \\ 0.998714e^{-i0.000\pi} \\ 0.993885e^{i0.003\pi} \\ 0.993885e^{-i0.003\pi} \\ 0.993869e^{i0.006\pi} \\ 0.993869e^{-i0.006\pi} \\ 0.992606 \\ 0.991243e^{i0.004\pi} \\ 0.991243e^{-i0.004\pi} \\ 0.988074e^{i0.000\pi} \\ 0.988074e^{-i0.000\pi} \\ 0.985941e^{i0.002\pi} \\ 0.985941e^{-i0.002\pi} \\ 0.985839e^{i0.006\pi} \\ 0.985839e^{-i0.006\pi} \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.02222e^{i0.422\pi} \\ 0.02222e^{i0.422\pi} \\ 0.046623e^{i0.386\pi} \\ 0.046623e^{i0.386\pi} \\ 0.042233e^{i0.370\pi} \\ 0.042233e^{i0.370\pi} \\ 0.099689 \\ 0.070182e^{i0.296\pi} \\ 0.070182e^{i0.296\pi} \\ 0.05523e^{i0.308\pi} \\ 0.05523e^{i0.308\pi} \\ 0.06728e^{i0.202\pi} \\ 0.06728e^{i0.202\pi} \\ 0.046658e^{i0.368\pi} \\ 0.046658e^{i0.368\pi} \end{pmatrix} $ $ \begin{pmatrix} 1 \\ 0.998714e^{i0.000\pi} \\ 0.998714e^{-i0.000\pi} \\ 0.993885e^{i0.003\pi} \\ 0.993885e^{-i0.003\pi} \\ 0.993869e^{i0.006\pi} \\ 0.993869e^{-i0.006\pi} \\ 0.992606 \\ 0.991243e^{i0.004\pi} \\ 0.991243e^{-i0.004\pi} \\ 0.988074e^{i0.000\pi} \\ 0.988074e^{-i0.000\pi} \\ 0.985941e^{i0.002\pi} \\ 0.985941e^{-i0.002\pi} \\ 0.985839e^{i0.006\pi} \\ 0.985839e^{-i0.006\pi} \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.02222 \\ 0.02222 \\ 0.046623 \\ 0.046623 \\ 0.042233 \\ 0.042233 \\ 0.099689 \\ 0.070182 \\ 0.070182 \\ 0.05523 \\ 0.05523 \\ 0.06728 \\ 0.06728 \\ 0.046658 \\ 0.046658 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.00257 \\ 0.00257 \\ 0.012193 \\ 0.012193 \\ 0.012224 \\ 0.012224 \\ 0.014733 \\ 0.017438 \\ 0.017438 \\ 0.023711 \\ 0.023711 \\ 0.027921 \\ 0.027921 \\ 0.028122 \\ 0.028122 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.005399 \\ 0.005398 \\ 0.016393 \\ 0.016117 \\ 0.016967 \\ 0.01635 \\ 0.098952 \\ 0.042029 \\ 0.041071 \\ 0.031033 \\ 0.030972 \\ 0.053862 \\ 0.053096 \\ 0.01884 \\ 0.01812 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ -0.001287 \\ -0.001287 \\ -0.006134 \\ -0.006134 \\ -0.00615 \\ -0.00615 \\ -0.007422 \\ -0.008796 \\ -0.008796 \\ -0.011998 \\ -0.011998 \\ -0.014159 \\ -0.014159 \\ -0.014262 \\ -0.014262 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.00563 \\ 0.005625 \\ 0.017615 \\ 0.016894 \\ 0.018156 \\ 0.016762 \\ 0.095703 \\ 0.0435 \\ 0.042299 \\ 0.032297 \\ 0.032212 \\ 0.054546 \\ 0.054027 \\ 0.02055 \\ 0.018928 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.000039 \\ -0.000039 \\ 0.002706 \\ -0.002706 \\ 0.005895 \\ -0.005895 \\ 0 \\ 0.003668 \\ -0.003668 \\ 0.000315 \\ -0.000315 \\ 0.002279 \\ -0.002279 \\ 0.006197 \\ -0.006197 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0.006831 \\ 0.006831 \\ 0.013699 \\ 0.013796 \\ 0.012095 \\ 0.012307 \\ 0 \\ 0.017164 \\ 0.017483 \\ 0.014172 \\ 0.014193 \\ 0.012052 \\ 0.012296 \\ 0.013401 \\ 0.013654 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.00563 \\ 0.005625 \\ 0.017615 \\ 0.016894 \\ 0.018156 \\ 0.016762 \\ 0.095703 \\ 0.0435 \\ 0.042299 \\ 0.032297 \\ 0.032212 \\ 0.054546 \\ 0.054027 \\ 0.02055 \\ 0.018928 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0.006831 \\ 0.006831 \\ 0.013699 \\ 0.013796 \\ 0.012095 \\ 0.012307 \\ 0 \\ 0.017164 \\ 0.017483 \\ 0.014172 \\ 0.014193 \\ 0.012052 \\ 0.012296 \\ 0.013401 \\ 0.013654 \end{pmatrix} $ π
Gxpi2:1$ \begin{pmatrix} 1 \\ 0.9987 \\ 0.996318e^{i0.500\pi} \\ 0.996318e^{-i0.500\pi} \\ 0.996204e^{i0.500\pi} \\ 0.996204e^{-i0.500\pi} \\ 0.995062 \\ 0.992519 \\ 0.988418 \\ 0.985917 \\ 0.985001e^{i0.500\pi} \\ 0.985001e^{-i0.500\pi} \\ 0.984622e^{i0.500\pi} \\ 0.984622e^{-i0.500\pi} \\ 0.982011e^{i0.000\pi} \\ 0.982011e^{-i0.000\pi} \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.003619 \\ 0.009203e^{i0.125\pi} \\ 0.009203e^{i0.125\pi} \\ 0.01311e^{i0.170\pi} \\ 0.01311e^{i0.170\pi} \\ 0.005307 \\ 0.077538 \\ 0.094314 \\ 0.043156 \\ 0.031025e^{i0.364\pi} \\ 0.031025e^{i0.364\pi} \\ 0.044919e^{i0.256\pi} \\ 0.044919e^{i0.256\pi} \\ 0.02034e^{i0.335\pi} \\ 0.02034e^{i0.335\pi} \end{pmatrix} $ $ \begin{pmatrix} 1 \\ 0.9987 \\ 0.996318e^{i0.500\pi} \\ 0.996318e^{-i0.500\pi} \\ 0.996204e^{i0.500\pi} \\ 0.996204e^{-i0.500\pi} \\ 0.995062 \\ 0.992519 \\ 0.988418 \\ 0.985917 \\ 0.985001e^{i0.500\pi} \\ 0.985001e^{-i0.500\pi} \\ 0.984622e^{i0.500\pi} \\ 0.984622e^{-i0.500\pi} \\ 0.982011e^{i0.000\pi} \\ 0.982011e^{-i0.000\pi} \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.003619 \\ 0.009203 \\ 0.009203 \\ 0.01311 \\ 0.01311 \\ 0.005307 \\ 0.077538 \\ 0.094314 \\ 0.043156 \\ 0.031025 \\ 0.031025 \\ 0.044919 \\ 0.044919 \\ 0.02034 \\ 0.02034 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.002599 \\ 0.00735 \\ 0.00735 \\ 0.007577 \\ 0.007577 \\ 0.009852 \\ 0.014906 \\ 0.02303 \\ 0.027968 \\ 0.029773 \\ 0.029773 \\ 0.030519 \\ 0.030519 \\ 0.035655 \\ 0.035655 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.003614 \\ 0.008461 \\ 0.008471 \\ 0.011253 \\ 0.011234 \\ 0.005281 \\ 0.076958 \\ 0.093222 \\ 0.042548 \\ 0.012626 \\ 0.012646 \\ 0.03072 \\ 0.030657 \\ 0.009896 \\ 0.009875 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ -0.001301 \\ -0.003689 \\ -0.003689 \\ -0.003803 \\ -0.003803 \\ -0.00495 \\ -0.007509 \\ -0.011649 \\ -0.014183 \\ -0.015112 \\ -0.015112 \\ -0.015497 \\ -0.015497 \\ -0.018153 \\ -0.018153 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.003617 \\ 0.003572 \\ -0.003522 \\ 0.006745 \\ -0.006643 \\ 0.005319 \\ 0.075221 \\ 0.091137 \\ 0.042842 \\ 0.028346 \\ -0.029019 \\ 0.032824 \\ -0.032834 \\ 0.010376 \\ 0.010339 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0.500184 \\ -0.500184 \\ 0.499738 \\ -0.499738 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0.500251 \\ -0.500251 \\ 0.499672 \\ -0.499672 \\ 0.000331 \\ -0.000331 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ -0.002706 \\ 0.002724 \\ -0.00358 \\ 0.003632 \\ 0 \\ 0 \\ 0 \\ 0 \\ -0.004037 \\ 0.00426 \\ -0.009742 \\ 0.010425 \\ 0.005667 \\ 0.005674 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.003617 \\ 0.003572 \\ 0.003522 \\ 0.006745 \\ 0.006643 \\ 0.005319 \\ 0.075221 \\ 0.091137 \\ 0.042842 \\ 0.028346 \\ 0.029019 \\ 0.032824 \\ 0.032834 \\ 0.010376 \\ 0.010339 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0.002706 \\ 0.002724 \\ 0.00358 \\ 0.003632 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0.004037 \\ 0.00426 \\ 0.009742 \\ 0.010425 \\ 0.005667 \\ 0.005674 \end{pmatrix} $ π
Gxpi2:0$ \begin{pmatrix} 1 \\ 0.997864 \\ 0.993764e^{i0.505\pi} \\ 0.993764e^{-i0.505\pi} \\ 0.993697e^{i0.511\pi} \\ 0.993697e^{-i0.511\pi} \\ 0.989939e^{i0.518\pi} \\ 0.989939e^{-i0.518\pi} \\ 0.989934e^{i0.499\pi} \\ 0.989934e^{-i0.499\pi} \\ 0.989915e^{i0.012\pi} \\ 0.989915e^{-i0.012\pi} \\ 0.989722 \\ 0.989652e^{i0.007\pi} \\ 0.989652e^{-i0.007\pi} \\ 0.988364 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.00878 \\ 0.008449e^{i0.334\pi} \\ 0.008449e^{i0.334\pi} \\ 0.012314e^{i0.259\pi} \\ 0.012314e^{i0.259\pi} \\ 0.034277e^{i0.312\pi} \\ 0.034277e^{i0.312\pi} \\ 0.024184e^{i0.192\pi} \\ 0.024184e^{i0.192\pi} \\ 0.034863e^{i0.265\pi} \\ 0.034863e^{i0.265\pi} \\ 0.009148 \\ 0.055108e^{i0.418\pi} \\ 0.055108e^{i0.418\pi} \\ 0.013582 \end{pmatrix} $ $ \begin{pmatrix} 1 \\ 0.997864 \\ 0.993764e^{i0.505\pi} \\ 0.993764e^{-i0.505\pi} \\ 0.993697e^{i0.511\pi} \\ 0.993697e^{-i0.511\pi} \\ 0.989939e^{i0.518\pi} \\ 0.989939e^{-i0.518\pi} \\ 0.989934e^{i0.499\pi} \\ 0.989934e^{-i0.499\pi} \\ 0.989915e^{i0.012\pi} \\ 0.989915e^{-i0.012\pi} \\ 0.989722 \\ 0.989652e^{i0.007\pi} \\ 0.989652e^{-i0.007\pi} \\ 0.988364 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.00878 \\ 0.008449 \\ 0.008449 \\ 0.012314 \\ 0.012314 \\ 0.034277 \\ 0.034277 \\ 0.024184 \\ 0.024184 \\ 0.034863 \\ 0.034863 \\ 0.009148 \\ 0.055108 \\ 0.055108 \\ 0.013582 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.004267 \\ 0.012432 \\ 0.012432 \\ 0.012565 \\ 0.012565 \\ 0.02002 \\ 0.02002 \\ 0.020031 \\ 0.020031 \\ 0.020069 \\ 0.020069 \\ 0.02045 \\ 0.020589 \\ 0.020589 \\ 0.023137 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.008761 \\ 0.004115 \\ 0.00425 \\ 0.008097 \\ 0.008688 \\ 0.017814 \\ 0.019906 \\ 0.019811 \\ 0.019649 \\ 0.024086 \\ 0.022299 \\ 0.009054 \\ 0.014253 \\ 0.013668 \\ 0.013424 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ -0.002138 \\ -0.006255 \\ -0.006255 \\ -0.006322 \\ -0.006322 \\ -0.010112 \\ -0.010112 \\ -0.010117 \\ -0.010117 \\ -0.010136 \\ -0.010136 \\ -0.010331 \\ -0.010402 \\ -0.010402 \\ -0.011705 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.00876 \\ 0.007285 \\ -0.007458 \\ 0.008709 \\ -0.009316 \\ 0.027483 \\ -0.030075 \\ 0.01402 \\ -0.01364 \\ 0.024672 \\ 0.022759 \\ 0.009201 \\ 0.016652 \\ 0.014466 \\ 0.013648 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0.505124 \\ -0.505124 \\ 0.511209 \\ -0.511209 \\ 0.517641 \\ -0.517641 \\ 0.498692 \\ -0.498692 \\ 0.012255 \\ -0.012255 \\ 0 \\ 0.006668 \\ -0.006668 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ -0.001376 \\ 0.00132 \\ -0.002782 \\ 0.002629 \\ -0.006454 \\ 0.005791 \\ -0.006302 \\ 0.006516 \\ 0.007806 \\ 0.008388 \\ 0 \\ 0.016761 \\ 0.016986 \\ 0 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.00876 \\ 0.007285 \\ 0.007458 \\ 0.008709 \\ 0.009316 \\ 0.027483 \\ 0.030075 \\ 0.01402 \\ 0.01364 \\ 0.024672 \\ 0.022759 \\ 0.009201 \\ 0.016652 \\ 0.014466 \\ 0.013648 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0.001376 \\ 0.00132 \\ 0.002782 \\ 0.002629 \\ 0.006454 \\ 0.005791 \\ 0.006302 \\ 0.006516 \\ 0.007806 \\ 0.008388 \\ 0 \\ 0.016761 \\ 0.016986 \\ 0 \end{pmatrix} $ π
Gypi2:1$ \begin{pmatrix} 1 \\ 0.997035 \\ 0.99454e^{i0.502\pi} \\ 0.99454e^{-i0.502\pi} \\ 0.990289e^{i0.009\pi} \\ 0.990289e^{-i0.009\pi} \\ 0.989971e^{i0.012\pi} \\ 0.989971e^{-i0.012\pi} \\ 0.988971e^{i0.512\pi} \\ 0.988971e^{-i0.512\pi} \\ 0.988921e^{i0.491\pi} \\ 0.988921e^{-i0.491\pi} \\ 0.985644 \\ 0.984269e^{i0.502\pi} \\ 0.984269e^{-i0.502\pi} \\ 0.98339 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.010709 \\ 0.016056e^{i0.308\pi} \\ 0.016056e^{i0.308\pi} \\ 0.030592e^{i0.157\pi} \\ 0.030592e^{i0.157\pi} \\ 0.034405e^{i0.146\pi} \\ 0.034405e^{i0.146\pi} \\ 0.062388e^{i0.187\pi} \\ 0.062388e^{i0.187\pi} \\ 0.040223e^{i0.084\pi} \\ 0.040223e^{i0.084\pi} \\ 0.014925 \\ 0.121571e^{i0.056\pi} \\ 0.121571e^{i0.056\pi} \\ 0.063247 \end{pmatrix} $ $ \begin{pmatrix} 1 \\ 0.997035 \\ 0.99454e^{i0.502\pi} \\ 0.99454e^{-i0.502\pi} \\ 0.990289e^{i0.009\pi} \\ 0.990289e^{-i0.009\pi} \\ 0.989971e^{i0.012\pi} \\ 0.989971e^{-i0.012\pi} \\ 0.988971e^{i0.512\pi} \\ 0.988971e^{-i0.512\pi} \\ 0.988921e^{i0.491\pi} \\ 0.988921e^{-i0.491\pi} \\ 0.985644 \\ 0.984269e^{i0.502\pi} \\ 0.984269e^{-i0.502\pi} \\ 0.98339 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.010709 \\ 0.016056 \\ 0.016056 \\ 0.030592 \\ 0.030592 \\ 0.034405 \\ 0.034405 \\ 0.062388 \\ 0.062388 \\ 0.040223 \\ 0.040223 \\ 0.014925 \\ 0.121571 \\ 0.121571 \\ 0.063247 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.005921 \\ 0.01089 \\ 0.01089 \\ 0.019329 \\ 0.019329 \\ 0.019957 \\ 0.019957 \\ 0.021936 \\ 0.021936 \\ 0.022035 \\ 0.022035 \\ 0.028506 \\ 0.031215 \\ 0.031215 \\ 0.032944 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.010678 \\ 0.009033 \\ 0.00912 \\ 0.027419 \\ 0.025895 \\ 0.031643 \\ 0.02935 \\ 0.049415 \\ 0.053303 \\ 0.039475 \\ 0.037301 \\ 0.01471 \\ 0.117241 \\ 0.118357 \\ 0.062197 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ -0.002969 \\ -0.005475 \\ -0.005475 \\ -0.009759 \\ -0.009759 \\ -0.01008 \\ -0.01008 \\ -0.01109 \\ -0.01109 \\ -0.011141 \\ -0.011141 \\ -0.01446 \\ -0.015856 \\ -0.015856 \\ -0.01675 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.010684 \\ 0.013193 \\ -0.013373 \\ 0.027318 \\ 0.026525 \\ 0.0313 \\ 0.03021 \\ 0.033717 \\ -0.036151 \\ 0.012379 \\ -0.008731 \\ 0.015028 \\ 0.02794 \\ -0.01485 \\ 0.062332 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0.501519 \\ -0.501519 \\ 0.009095 \\ -0.009095 \\ 0.011962 \\ -0.011962 \\ 0.512043 \\ -0.512043 \\ 0.490987 \\ -0.490987 \\ 0 \\ 0.501508 \\ -0.501508 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ -0.002903 \\ 0.00294 \\ 0.004297 \\ 0.004783 \\ 0.004397 \\ 0.005125 \\ -0.016574 \\ 0.016902 \\ -0.01225 \\ 0.012704 \\ 0 \\ -0.037759 \\ 0.039351 \\ 0 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.010684 \\ 0.013193 \\ 0.013373 \\ 0.027318 \\ 0.026525 \\ 0.0313 \\ 0.03021 \\ 0.033717 \\ 0.036151 \\ 0.012379 \\ 0.008731 \\ 0.015028 \\ 0.02794 \\ 0.01485 \\ 0.062332 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0.002903 \\ 0.00294 \\ 0.004297 \\ 0.004783 \\ 0.004397 \\ 0.005125 \\ 0.016574 \\ 0.016902 \\ 0.01225 \\ 0.012704 \\ 0 \\ 0.037759 \\ 0.039351 \\ 0 \end{pmatrix} $ π
Gypi2:0$ \begin{pmatrix} 1 \\ 0.999002 \\ 0.996094e^{i0.503\pi} \\ 0.996094e^{-i0.503\pi} \\ 0.996014e^{i0.507\pi} \\ 0.996014e^{-i0.507\pi} \\ 0.992873 \\ 0.992701 \\ 0.983344e^{i0.518\pi} \\ 0.983344e^{-i0.518\pi} \\ 0.983296e^{i0.015\pi} \\ 0.983296e^{-i0.015\pi} \\ 0.983063e^{i0.011\pi} \\ 0.983063e^{-i0.011\pi} \\ 0.983052e^{i0.492\pi} \\ 0.983052e^{-i0.492\pi} \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.003308 \\ 0.009424e^{i0.187\pi} \\ 0.009424e^{i0.187\pi} \\ 0.021644e^{i0.074\pi} \\ 0.021644e^{i0.074\pi} \\ 0.02175 \\ 0.034408 \\ 0.059387e^{i0.446\pi} \\ 0.059387e^{i0.446\pi} \\ 0.074565e^{i0.208\pi} \\ 0.074565e^{i0.208\pi} \\ 0.041644e^{i0.259\pi} \\ 0.041644e^{i0.259\pi} \\ 0.042314e^{i0.321\pi} \\ 0.042314e^{i0.321\pi} \end{pmatrix} $ $ \begin{pmatrix} 1 \\ 0.999002 \\ 0.996094e^{i0.503\pi} \\ 0.996094e^{-i0.503\pi} \\ 0.996014e^{i0.507\pi} \\ 0.996014e^{-i0.507\pi} \\ 0.992873 \\ 0.992701 \\ 0.983344e^{i0.518\pi} \\ 0.983344e^{-i0.518\pi} \\ 0.983296e^{i0.015\pi} \\ 0.983296e^{-i0.015\pi} \\ 0.983063e^{i0.011\pi} \\ 0.983063e^{-i0.011\pi} \\ 0.983052e^{i0.492\pi} \\ 0.983052e^{-i0.492\pi} \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.003308 \\ 0.009424 \\ 0.009424 \\ 0.021644 \\ 0.021644 \\ 0.02175 \\ 0.034408 \\ 0.059387 \\ 0.059387 \\ 0.074565 \\ 0.074565 \\ 0.041644 \\ 0.041644 \\ 0.042314 \\ 0.042314 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.001995 \\ 0.007797 \\ 0.007797 \\ 0.007957 \\ 0.007957 \\ 0.014204 \\ 0.014544 \\ 0.033034 \\ 0.033034 \\ 0.033129 \\ 0.033129 \\ 0.033587 \\ 0.033587 \\ 0.033608 \\ 0.033608 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.003304 \\ 0.007745 \\ 0.007887 \\ 0.0205 \\ 0.02144 \\ 0.021595 \\ 0.034156 \\ 0.00924 \\ 0.010339 \\ 0.060901 \\ 0.055537 \\ 0.029116 \\ 0.027171 \\ 0.022717 \\ 0.02163 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ -0.000998 \\ -0.003914 \\ -0.003914 \\ -0.003994 \\ -0.003994 \\ -0.007153 \\ -0.007326 \\ -0.016796 \\ -0.016796 \\ -0.016845 \\ -0.016845 \\ -0.017082 \\ -0.017082 \\ -0.017093 \\ -0.017093 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.003305 \\ 0.005184 \\ -0.005293 \\ 0.004755 \\ -0.005281 \\ 0.021669 \\ 0.034073 \\ 0.057286 \\ -0.06186 \\ 0.061291 \\ 0.057531 \\ 0.030153 \\ 0.028149 \\ 0.036524 \\ -0.036192 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0.502902 \\ -0.502902 \\ 0.507134 \\ -0.507134 \\ 0 \\ 0 \\ 0.517844 \\ -0.517844 \\ 0.014652 \\ -0.014652 \\ 0.010997 \\ -0.010997 \\ 0.492193 \\ -0.492193 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ -0.00251 \\ 0.002506 \\ -0.006733 \\ 0.006729 \\ 0 \\ 0 \\ -0.004046 \\ 0.002299 \\ 0.012934 \\ 0.014651 \\ 0.009182 \\ 0.009823 \\ -0.006768 \\ 0.007868 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.003305 \\ 0.005184 \\ 0.005293 \\ 0.004755 \\ 0.005281 \\ 0.021669 \\ 0.034073 \\ 0.057286 \\ 0.06186 \\ 0.061291 \\ 0.057531 \\ 0.030153 \\ 0.028149 \\ 0.036524 \\ 0.036192 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0.00251 \\ 0.002506 \\ 0.006733 \\ 0.006729 \\ 0 \\ 0 \\ 0.004046 \\ 0.002299 \\ 0.012934 \\ 0.014651 \\ 0.009182 \\ 0.009823 \\ 0.006768 \\ 0.007868 \end{pmatrix} $ π
Gcphase:0:1$ \begin{pmatrix} 1 \\ 0.998557 \\ 0.995251 \\ 0.993616 \\ 0.982655e^{i0.017\pi} \\ 0.982655e^{-i0.017\pi} \\ 0.982559e^{i0.009\pi} \\ 0.982559e^{-i0.009\pi} \\ 0.982034e^{i0.982\pi} \\ 0.982034e^{-i0.982\pi} \\ 0.981637e^{i0.974\pi} \\ 0.981637e^{-i0.974\pi} \\ 0.968119e^{i0.007\pi} \\ 0.968119e^{-i0.007\pi} \\ 0.967627e^{i0.991\pi} \\ 0.967627e^{-i0.991\pi} \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.00506 \\ 0.024844 \\ 0.012188 \\ 0.05446e^{i0.154\pi} \\ 0.05446e^{i0.154\pi} \\ 0.029927e^{i0.115\pi} \\ 0.029927e^{i0.115\pi} \\ 0.026108e^{i0.316\pi} \\ 0.026108e^{i0.316\pi} \\ 0.060803e^{i0.249\pi} \\ 0.060803e^{i0.249\pi} \\ 0.045035e^{i0.412\pi} \\ 0.045035e^{i0.412\pi} \\ 0.096531e^{i0.422\pi} \\ 0.096531e^{i0.422\pi} \end{pmatrix} $ $ \begin{pmatrix} 1 \\ 0.998557 \\ 0.995251 \\ 0.993616 \\ 0.982655e^{i0.017\pi} \\ 0.982655e^{-i0.017\pi} \\ 0.982559e^{i0.009\pi} \\ 0.982559e^{-i0.009\pi} \\ 0.982034e^{i0.982\pi} \\ 0.982034e^{-i0.982\pi} \\ 0.981637e^{i0.974\pi} \\ 0.981637e^{-i0.974\pi} \\ 0.968119e^{i0.007\pi} \\ 0.968119e^{-i0.007\pi} \\ 0.967627e^{i0.991\pi} \\ 0.967627e^{-i0.991\pi} \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.00506 \\ 0.024844 \\ 0.012188 \\ 0.05446 \\ 0.05446 \\ 0.029927 \\ 0.029927 \\ 0.026108 \\ 0.026108 \\ 0.060803 \\ 0.060803 \\ 0.045035 \\ 0.045035 \\ 0.096531 \\ 0.096531 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.002885 \\ 0.009475 \\ 0.012728 \\ 0.034389 \\ 0.034389 \\ 0.034579 \\ 0.034579 \\ 0.035609 \\ 0.035609 \\ 0.036388 \\ 0.036388 \\ 0.062746 \\ 0.062746 \\ 0.063697 \\ 0.063697 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.005053 \\ 0.024726 \\ 0.01211 \\ 0.049843 \\ 0.044773 \\ 0.028299 \\ 0.02666 \\ 0.013147 \\ 0.014769 \\ 0.038765 \\ 0.045682 \\ 0.012234 \\ 0.011687 \\ 0.022021 \\ 0.023302 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ -0.001445 \\ -0.00476 \\ -0.006405 \\ -0.017497 \\ -0.017497 \\ -0.017595 \\ -0.017595 \\ -0.018129 \\ -0.018129 \\ -0.018533 \\ -0.018533 \\ -0.0324 \\ -0.0324 \\ -0.032908 \\ -0.032908 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.005055 \\ 0.024656 \\ 0.012192 \\ 0.049386 \\ 0.046881 \\ 0.028426 \\ 0.027817 \\ -0.012995 \\ -0.015655 \\ -0.039888 \\ -0.047663 \\ 0.014649 \\ 0.012659 \\ -0.016771 \\ -0.022458 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0.017039 \\ -0.017039 \\ 0.009491 \\ -0.009491 \\ 0.98153 \\ -0.98153 \\ 0.973987 \\ -0.973987 \\ 0.007277 \\ -0.007277 \\ 0.991007 \\ -0.991007 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0.007003 \\ 0.008616 \\ 0.00308 \\ 0.003607 \\ -0.007446 \\ -0.006922 \\ -0.0156 \\ -0.013324 \\ 0.013941 \\ 0.014152 \\ -0.031587 \\ 1.96868 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.005055 \\ 0.024656 \\ 0.012192 \\ 0.049386 \\ 0.046881 \\ 0.028426 \\ 0.027817 \\ 0.012995 \\ 0.015655 \\ 0.039888 \\ 0.047663 \\ 0.014649 \\ 0.012659 \\ 0.016771 \\ 0.022458 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0.007003 \\ 0.008616 \\ 0.00308 \\ 0.003607 \\ 0.007446 \\ 0.006922 \\ 0.0156 \\ 0.013324 \\ 0.013941 \\ 0.014152 \\ 0.031587 \\ 1.96868 \end{pmatrix} $ π
Qubit 0 ---|Gxpi2|-|Gypi2|--- Qubit 1 ---| |-| |--- $ \begin{pmatrix} 1 \\ 0.995962 \\ 0.988919 \\ 0.987067e^{i0.680\pi} \\ 0.987067e^{-i0.680\pi} \\ 0.985827e^{i0.678\pi} \\ 0.985827e^{-i0.678\pi} \\ 0.985772 \\ 0.979111e^{i0.022\pi} \\ 0.979111e^{-i0.022\pi} \\ 0.97333e^{i0.022\pi} \\ 0.97333e^{-i0.022\pi} \\ 0.971183e^{i0.701\pi} \\ 0.971183e^{-i0.701\pi} \\ 0.97097e^{i0.657\pi} \\ 0.97097e^{-i0.657\pi} \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.007162 \\ 0.020505 \\ 0.042873e^{i0.316\pi} \\ 0.042873e^{i0.316\pi} \\ 0.040824e^{i0.327\pi} \\ 0.040824e^{i0.327\pi} \\ 0.029279 \\ 0.059198e^{i0.281\pi} \\ 0.059198e^{i0.281\pi} \\ 0.114171e^{i0.300\pi} \\ 0.114171e^{i0.300\pi} \\ 0.072115e^{i0.260\pi} \\ 0.072115e^{i0.260\pi} \\ 0.113361e^{i0.347\pi} \\ 0.113361e^{i0.347\pi} \end{pmatrix} $ $ \begin{pmatrix} 1 \\ 0.996706 \\ 0.987977 \\ 0.987009e^{i0.677\pi} \\ 0.987009e^{-i0.677\pi} \\ 0.987023e^{i0.671\pi} \\ 0.987023e^{-i0.671\pi} \\ 0.986092 \\ 0.975384e^{i0.019\pi} \\ 0.975384e^{-i0.019\pi} \\ 0.975905e^{i0.024\pi} \\ 0.975905e^{-i0.024\pi} \\ 0.971134e^{i0.696\pi} \\ 0.971134e^{-i0.696\pi} \\ 0.97098e^{i0.652\pi} \\ 0.97098e^{-i0.652\pi} \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.000744 \\ 0.000942 \\ 0.009745 \\ 0.009745 \\ 0.021284 \\ 0.021284 \\ 0.00032 \\ 0.009003 \\ 0.009003 \\ 0.007286 \\ 0.007286 \\ 0.015968 \\ 0.015968 \\ 0.01458 \\ 0.01458 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.007162 \\ 0.020505 \\ 0.042873 \\ 0.042873 \\ 0.040824 \\ 0.040824 \\ 0.029279 \\ 0.059198 \\ 0.059198 \\ 0.114171 \\ 0.114171 \\ 0.072115 \\ 0.072115 \\ 0.113361 \\ 0.113361 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.007318 \\ 0.022971 \\ 0.025804 \\ 0.025804 \\ 0.027191 \\ 0.027191 \\ 0.027938 \\ 0.045025 \\ 0.045025 \\ 0.050146 \\ 0.050146 \\ 0.056979 \\ 0.056979 \\ 0.057313 \\ 0.057313 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.007139 \\ 0.020259 \\ 0.007423 \\ 0.031875 \\ 0.007216 \\ 0.028603 \\ 0.028871 \\ 0.038893 \\ 0.034409 \\ 0.070453 \\ 0.060374 \\ 0.011419 \\ 0.06694 \\ 0.021796 \\ 0.068763 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ -0.004046 \\ -0.011143 \\ -0.013017 \\ -0.013017 \\ -0.014274 \\ -0.014274 \\ -0.01433 \\ -0.02111 \\ -0.02111 \\ -0.027032 \\ -0.027032 \\ -0.02924 \\ -0.02924 \\ -0.029459 \\ -0.029459 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.007166 \\ 0.020523 \\ 0.018531 \\ -0.044403 \\ 0.019125 \\ -0.042287 \\ 0.029269 \\ 0.04164 \\ 0.035644 \\ 0.076276 \\ 0.064776 \\ 0.015971 \\ -0.076506 \\ 0.067531 \\ -0.124137 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0.680314 \\ -0.680314 \\ 0.678196 \\ -0.678196 \\ 0 \\ 0.022115 \\ -0.022115 \\ 0.022248 \\ -0.022248 \\ 0.701451 \\ -0.701451 \\ 0.657073 \\ -0.657073 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ -0.012364 \\ 0.000176 \\ -0.01155 \\ -0.000216 \\ 0 \\ 0.013401 \\ 0.015124 \\ 0.026502 \\ 0.029699 \\ -0.022895 \\ 0.00312 \\ -0.028796 \\ -0.000489 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0.000747 \\ 0.000953 \\ 0.000059 \\ 0.000059 \\ 0.001213 \\ 0.001213 \\ 0.000324 \\ 0.003814 \\ 0.003814 \\ 0.002642 \\ 0.002642 \\ 0.000051 \\ 0.000051 \\ 0.00001 \\ 0.00001 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.007166 \\ 0.020523 \\ 0.018531 \\ 0.044403 \\ 0.019125 \\ 0.042287 \\ 0.029269 \\ 0.04164 \\ 0.035644 \\ 0.076276 \\ 0.064776 \\ 0.015971 \\ 0.076506 \\ 0.067531 \\ 0.124137 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0.003143 \\ 0.003143 \\ 0.006857 \\ 0.006857 \\ 0 \\ 0.002669 \\ 0.002669 \\ 0.002226 \\ 0.002226 \\ 0.005234 \\ 0.005234 \\ 0.00478 \\ 0.00478 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0.012364 \\ 0.000176 \\ 0.01155 \\ 0.000216 \\ 0 \\ 0.013401 \\ 0.015124 \\ 0.026502 \\ 0.029699 \\ 0.022895 \\ 0.00312 \\ 0.028796 \\ 0.000489 \end{pmatrix} $ π
Qubit 0 ---| |-| |--- Qubit 1 ---|Gxpi2|-|Gypi2|--- $ \begin{pmatrix} 1 \\ 0.992912 \\ 0.983501e^{i0.667\pi} \\ 0.983501e^{-i0.667\pi} \\ 0.980519e^{i0.005\pi} \\ 0.980519e^{-i0.005\pi} \\ 0.980362e^{i0.014\pi} \\ 0.980362e^{-i0.014\pi} \\ 0.979734e^{i0.657\pi} \\ 0.979734e^{-i0.657\pi} \\ 0.979709e^{i0.678\pi} \\ 0.979709e^{-i0.678\pi} \\ 0.977076e^{i0.668\pi} \\ 0.977076e^{-i0.668\pi} \\ 0.968146 \\ 0.967558 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.01368 \\ 0.177503e^{i0.145\pi} \\ 0.177503e^{i0.145\pi} \\ 0.04239e^{i0.284\pi} \\ 0.04239e^{i0.284\pi} \\ 0.041609e^{i0.243\pi} \\ 0.041609e^{i0.243\pi} \\ 0.051267e^{i0.066\pi} \\ 0.051267e^{i0.066\pi} \\ 0.093376e^{i0.266\pi} \\ 0.093376e^{i0.266\pi} \\ 0.250042e^{i0.138\pi} \\ 0.250042e^{i0.138\pi} \\ 0.074431 \\ 0.027949 \end{pmatrix} $ $ \begin{pmatrix} 1 \\ 0.993035 \\ 0.992584e^{i0.668\pi} \\ 0.992584e^{-i0.668\pi} \\ 0.980856e^{i0.009\pi} \\ 0.980856e^{-i0.009\pi} \\ 0.980368e^{i0.011\pi} \\ 0.980368e^{-i0.011\pi} \\ 0.979407e^{i0.658\pi} \\ 0.979407e^{-i0.658\pi} \\ 0.979479e^{i0.678\pi} \\ 0.979479e^{-i0.678\pi} \\ 0.968307e^{i0.668\pi} \\ 0.968307e^{-i0.668\pi} \\ 0.968061 \\ 0.967602 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.000123 \\ 0.009097 \\ 0.009097 \\ 0.010386 \\ 0.010386 \\ 0.01036 \\ 0.01036 \\ 0.000893 \\ 0.000893 \\ 0.00043 \\ 0.00043 \\ 0.008769 \\ 0.008769 \\ 0.000084 \\ 0.000043 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.01368 \\ 0.177503 \\ 0.177503 \\ 0.04239 \\ 0.04239 \\ 0.041609 \\ 0.041609 \\ 0.051267 \\ 0.051267 \\ 0.093376 \\ 0.093376 \\ 0.250042 \\ 0.250042 \\ 0.074431 \\ 0.027949 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.014004 \\ 0.023793 \\ 0.023793 \\ 0.038306 \\ 0.038306 \\ 0.038938 \\ 0.038938 \\ 0.040443 \\ 0.040443 \\ 0.040395 \\ 0.040395 \\ 0.05389 \\ 0.05389 \\ 0.062776 \\ 0.063789 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.013584 \\ 0.057357 \\ 0.216387 \\ 0.026803 \\ 0.025377 \\ 0.030458 \\ 0.028454 \\ 0.019902 \\ 0.066573 \\ 0.019578 \\ 0.084479 \\ 0.079564 \\ 0.300166 \\ 0.072054 \\ 0.027043 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ -0.007113 \\ -0.016637 \\ -0.016637 \\ -0.019673 \\ -0.019673 \\ -0.019833 \\ -0.019833 \\ -0.020475 \\ -0.020475 \\ -0.020499 \\ -0.020499 \\ -0.023191 \\ -0.023191 \\ -0.032373 \\ -0.032979 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.013683 \\ 0.003439 \\ -0.155496 \\ 0.027842 \\ 0.026776 \\ 0.031809 \\ 0.02935 \\ -0.013596 \\ -0.033508 \\ 0.029788 \\ -0.098352 \\ 0.009298 \\ -0.218587 \\ 0.074068 \\ 0.028476 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0.667359 \\ -0.667359 \\ 0.005326 \\ -0.005326 \\ 0.014185 \\ -0.014185 \\ 0.657265 \\ -0.657265 \\ 0.67763 \\ -0.67763 \\ 0.667529 \\ -0.667529 \\ 0 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ -0.057418 \\ 0.03745 \\ 0.010278 \\ 0.01057 \\ 0.008618 \\ 0.009485 \\ -0.016204 \\ 0.013158 \\ -0.028355 \\ 0.005887 \\ -0.081247 \\ 0.058358 \\ 0 \\ 0 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0.000124 \\ 0.009193 \\ 0.009193 \\ 0.000344 \\ 0.000344 \\ 0.000006 \\ 0.000006 \\ 0.000334 \\ 0.000334 \\ 0.000235 \\ 0.000235 \\ 0.009015 \\ 0.009015 \\ 0.000087 \\ 0.000045 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.013683 \\ 0.003439 \\ 0.155496 \\ 0.027842 \\ 0.026776 \\ 0.031809 \\ 0.02935 \\ 0.013596 \\ 0.033508 \\ 0.029788 \\ 0.098352 \\ 0.009298 \\ 0.218587 \\ 0.074068 \\ 0.028476 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0.000164 \\ 0.000164 \\ 0.003369 \\ 0.003369 \\ 0.003364 \\ 0.003364 \\ 0.00027 \\ 0.00027 \\ 0.000118 \\ 0.000118 \\ 0.000005 \\ 0.000005 \\ 0 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0.057418 \\ 0.03745 \\ 0.010278 \\ 0.01057 \\ 0.008618 \\ 0.009485 \\ 0.016204 \\ 0.013158 \\ 0.028355 \\ 0.005887 \\ 0.081247 \\ 0.058358 \\ 0 \\ 0 \end{pmatrix} $ π
Qubit 0 ---|Gxpi2|-|Gxpi2|-|Gypi2|--- Qubit 1 ---| |-| |-| |--- $ \begin{pmatrix} 1 \\ 0.993801 \\ 0.981702 \\ 0.980332e^{i0.981\pi} \\ 0.980332e^{-i0.981\pi} \\ 0.977851e^{i0.984\pi} \\ 0.977851e^{-i0.984\pi} \\ 0.975741 \\ 0.97126e^{i0.031\pi} \\ 0.97126e^{-i0.031\pi} \\ 0.963254e^{i0.031\pi} \\ 0.963254e^{-i0.031\pi} \\ 0.960549e^{i0.951\pi} \\ 0.960549e^{-i0.951\pi} \\ 0.960221e^{i0.986\pi} \\ 0.960221e^{-i0.986\pi} \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.009384 \\ 0.015198 \\ 0.041006e^{i0.350\pi} \\ 0.041006e^{i0.350\pi} \\ 0.05084e^{i0.287\pi} \\ 0.05084e^{i0.287\pi} \\ 0.025624 \\ 0.096579e^{i0.244\pi} \\ 0.096579e^{i0.244\pi} \\ 0.181851e^{i0.341\pi} \\ 0.181851e^{i0.341\pi} \\ 0.119732e^{i0.121\pi} \\ 0.119732e^{i0.121\pi} \\ 0.123037e^{i0.258\pi} \\ 0.123037e^{i0.258\pi} \end{pmatrix} $ $ \begin{pmatrix} 1 \\ 0.994588 \\ 0.980499 \\ 0.960182e^{i0.980\pi} \\ 0.960182e^{-i0.980\pi} \\ 0.979408e^{i0.984\pi} \\ 0.979408e^{-i0.984\pi} \\ 0.976931 \\ 0.966525e^{i0.028\pi} \\ 0.966525e^{-i0.028\pi} \\ 0.967364e^{i0.035\pi} \\ 0.967364e^{-i0.035\pi} \\ 0.960169e^{i0.957\pi} \\ 0.960169e^{-i0.957\pi} \\ 0.979434e^{i0.993\pi} \\ 0.979434e^{-i0.993\pi} \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.000788 \\ 0.001203 \\ 0.020181 \\ 0.020181 \\ 0.001585 \\ 0.001585 \\ 0.00119 \\ 0.011886 \\ 0.011886 \\ 0.01072 \\ 0.01072 \\ 0.018967 \\ 0.018967 \\ 0.027763 \\ 0.027763 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.009384 \\ 0.015198 \\ 0.041006 \\ 0.041006 \\ 0.05084 \\ 0.05084 \\ 0.025624 \\ 0.096579 \\ 0.096579 \\ 0.181851 \\ 0.181851 \\ 0.119732 \\ 0.119732 \\ 0.123037 \\ 0.123037 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.011577 \\ 0.037442 \\ 0.058703 \\ 0.058703 \\ 0.042286 \\ 0.042286 \\ 0.046769 \\ 0.061312 \\ 0.061312 \\ 0.068231 \\ 0.068231 \\ 0.077891 \\ 0.077891 \\ 0.059727 \\ 0.059727 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.009333 \\ 0.014901 \\ 0.016732 \\ 0.018952 \\ 0.02935 \\ 0.032381 \\ 0.025033 \\ 0.072819 \\ 0.061118 \\ 0.09267 \\ 0.074382 \\ 0.091491 \\ 0.120014 \\ 0.081089 \\ 0.084875 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ -0.006219 \\ -0.018468 \\ -0.019864 \\ -0.019864 \\ -0.022398 \\ -0.022398 \\ -0.024558 \\ -0.029161 \\ -0.029161 \\ -0.037438 \\ -0.037438 \\ -0.04025 \\ -0.04025 \\ -0.040591 \\ -0.040591 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.009398 \\ 0.015362 \\ -0.016065 \\ -0.020779 \\ -0.029731 \\ -0.03402 \\ 0.025922 \\ 0.076776 \\ 0.065014 \\ 0.1107 \\ 0.083771 \\ -0.1109 \\ -0.128959 \\ -0.082352 \\ -0.091964 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0.980585 \\ -0.980585 \\ 0.984285 \\ -0.984285 \\ 0 \\ 0.031318 \\ -0.031318 \\ 0.031442 \\ -0.031442 \\ 0.951046 \\ -0.951046 \\ 0.986162 \\ -0.986162 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ -0.01241 \\ -0.011716 \\ -0.013879 \\ -0.012888 \\ 0 \\ 0.018176 \\ 0.022596 \\ 0.044645 \\ 0.051139 \\ -0.022621 \\ -0.01018 \\ -0.033464 \\ 1.968903 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0.000792 \\ 0.001226 \\ 0.020768 \\ 0.020768 \\ 0.001591 \\ 0.001591 \\ 0.001219 \\ 0.004888 \\ 0.004888 \\ 0.004258 \\ 0.004258 \\ 0.000396 \\ 0.000396 \\ 0.019811 \\ 0.019811 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.009398 \\ 0.015362 \\ 0.016065 \\ 0.020779 \\ 0.029731 \\ 0.03402 \\ 0.025922 \\ 0.076776 \\ 0.065014 \\ 0.1107 \\ 0.083771 \\ 0.1109 \\ 0.128959 \\ 0.082352 \\ 0.091964 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0.000369 \\ 0.000369 \\ 0.000097 \\ 0.000097 \\ 0 \\ 0.003582 \\ 0.003582 \\ 0.003265 \\ 0.003265 \\ 0.006285 \\ 0.006285 \\ 0.006578 \\ 0.006578 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0.01241 \\ 0.011716 \\ 0.013879 \\ 0.012888 \\ 0 \\ 0.018176 \\ 0.022596 \\ 0.044645 \\ 0.051139 \\ 0.022621 \\ 0.01018 \\ 0.033464 \\ 1.968903 \end{pmatrix} $ π
Qubit 0 ---| |-| |-| |--- Qubit 1 ---|Gxpi2|-|Gxpi2|-|Gypi2|--- $ \begin{pmatrix} 1 \\ 0.987625 \\ -0.986755 \\ -0.985637 \\ 0.971103e^{i0.002\pi} \\ 0.971103e^{-i0.002\pi} \\ 0.970932e^{i0.013\pi} \\ 0.970932e^{-i0.013\pi} \\ 0.970364e^{i0.991\pi} \\ 0.970364e^{-i0.991\pi} \\ 0.970119e^{i0.991\pi} \\ 0.970119e^{-i0.991\pi} \\ -0.957703 \\ -0.956146 \\ 0.954285 \\ 0.949718 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.01336 \\ 0.032562 \\ 0.093503 \\ 0.115304e^{i0.422\pi} \\ 0.115304e^{i0.422\pi} \\ 0.046487e^{i0.290\pi} \\ 0.046487e^{i0.290\pi} \\ 0.089213e^{i0.207\pi} \\ 0.089213e^{i0.207\pi} \\ 0.096231e^{i0.273\pi} \\ 0.096231e^{i0.273\pi} \\ 0.122689 \\ 0.085182 \\ 0.097398 \\ 0.019119 \end{pmatrix} $ $ \begin{pmatrix} 1 \\ 0.988623 \\ -0.988673 \\ -0.990931 \\ 0.972595e^{i0.008\pi} \\ 0.972595e^{-i0.008\pi} \\ 0.969888e^{i0.010\pi} \\ 0.969888e^{-i0.010\pi} \\ 0.969933e^{i0.990\pi} \\ 0.969933e^{-i0.990\pi} \\ 0.970133e^{i0.991\pi} \\ 0.970133e^{-i0.991\pi} \\ -0.953677 \\ -0.952676 \\ 0.95332 \\ 0.950183 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.000998 \\ 0.001917 \\ 0.005294 \\ 0.018472 \\ 0.018472 \\ 0.011688 \\ 0.011688 \\ 0.000687 \\ 0.000687 \\ 0.000505 \\ 0.000505 \\ 0.004025 \\ 0.00347 \\ 0.000965 \\ 0.000466 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.01336 \\ 0.032562 \\ 0.093503 \\ 0.115304 \\ 0.115304 \\ 0.046487 \\ 0.046487 \\ 0.089213 \\ 0.089213 \\ 0.096231 \\ 0.096231 \\ 0.122689 \\ 0.085182 \\ 0.097398 \\ 0.019119 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.023611 \\ 0.024422 \\ 0.023301 \\ 0.055679 \\ 0.055679 \\ 0.058372 \\ 0.058372 \\ 0.058812 \\ 0.058812 \\ 0.058856 \\ 0.058856 \\ 0.086661 \\ 0.089103 \\ 0.090262 \\ 0.097594 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.013208 \\ 0.032194 \\ 0.092655 \\ 0.027797 \\ 0.026449 \\ 0.0285 \\ 0.026845 \\ 0.066823 \\ 0.070957 \\ 0.059344 \\ 0.062866 \\ 0.117005 \\ 0.081151 \\ 0.092851 \\ 0.018166 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ -0.012452 \\ -0.013333 \\ -0.014467 \\ -0.029322 \\ -0.029322 \\ -0.029499 \\ -0.029499 \\ -0.030084 \\ -0.030084 \\ -0.030337 \\ -0.030337 \\ -0.043218 \\ -0.044845 \\ -0.046793 \\ -0.051591 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.013437 \\ -0.033556 \\ -0.099672 \\ 0.035186 \\ 0.033918 \\ 0.031113 \\ 0.02813 \\ -0.07232 \\ -0.076117 \\ -0.061521 \\ -0.066341 \\ -0.137089 \\ -0.093311 \\ 0.097184 \\ 0.019931 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 1 \\ 1 \\ 0.001876 \\ -0.001876 \\ 0.013334 \\ -0.013334 \\ 0.990628 \\ -0.990628 \\ 0.990994 \\ -0.990994 \\ 1 \\ 1 \\ 0 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0.035424 \\ 0.035574 \\ 0.011273 \\ 0.012069 \\ -0.019764 \\ 1.981644 \\ -0.026019 \\ 1.975109 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0.00101 \\ 0.001941 \\ 0.005357 \\ 0.001535 \\ 0.001535 \\ 0.001076 \\ 0.001076 \\ 0.000444 \\ 0.000444 \\ 0.000015 \\ 0.000015 \\ 0.004212 \\ 0.003636 \\ 0.001012 \\ 0.00049 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.013437 \\ 0.033556 \\ 0.099672 \\ 0.035186 \\ 0.033918 \\ 0.031113 \\ 0.02813 \\ 0.07232 \\ 0.076117 \\ 0.061521 \\ 0.066341 \\ 0.137089 \\ 0.093311 \\ 0.097184 \\ 0.019931 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0.00603 \\ 0.00603 \\ 0.003819 \\ 0.003819 \\ 0.000176 \\ 0.000176 \\ 0.000165 \\ 0.000165 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0.035424 \\ 0.035574 \\ 0.011273 \\ 0.012069 \\ 0.019764 \\ 1.981644 \\ 0.026019 \\ 1.975109 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π
Qubit 0 ---| |-| |-|C1|--- Qubit 1 ---|Gxpi2|-|Gypi2|-|C0|--- $ \begin{pmatrix} 1 \\ 0.996204 \\ 0.980007 \\ 0.979024e^{i0.642\pi} \\ 0.979024e^{-i0.642\pi} \\ 0.978377 \\ 0.978299e^{i0.661\pi} \\ 0.978299e^{-i0.661\pi} \\ 0.944858e^{i0.851\pi} \\ 0.944858e^{-i0.851\pi} \\ 0.944852e^{i0.154\pi} \\ 0.944852e^{-i0.154\pi} \\ 0.941714e^{i0.488\pi} \\ 0.941714e^{-i0.488\pi} \\ 0.941446e^{i0.507\pi} \\ 0.941446e^{-i0.507\pi} \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.007263 \\ 0.036656 \\ 0.027412e^{i0.265\pi} \\ 0.027412e^{i0.265\pi} \\ 0.074416 \\ 0.024584e^{i0.222\pi} \\ 0.024584e^{i0.222\pi} \\ 0.101131e^{i0.342\pi} \\ 0.101131e^{i0.342\pi} \\ 0.10711e^{i0.210\pi} \\ 0.10711e^{i0.210\pi} \\ 0.132393e^{i0.096\pi} \\ 0.132393e^{i0.096\pi} \\ 0.13033e^{i0.335\pi} \\ 0.13033e^{i0.335\pi} \end{pmatrix} $ $ \begin{pmatrix} 1 \\ 0.996286 \\ 0.980069 \\ 0.979042e^{i0.652\pi} \\ 0.979042e^{-i0.652\pi} \\ 0.978522 \\ 0.978287e^{i0.661\pi} \\ 0.978287e^{-i0.661\pi} \\ 0.945618e^{i0.846\pi} \\ 0.945618e^{-i0.846\pi} \\ 0.945558e^{i0.159\pi} \\ 0.945558e^{-i0.159\pi} \\ 0.94081e^{i0.493\pi} \\ 0.94081e^{-i0.493\pi} \\ 0.940744e^{i0.502\pi} \\ 0.940744e^{-i0.502\pi} \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.000082 \\ 0.000063 \\ 0.030008 \\ 0.030008 \\ 0.000145 \\ 0.000032 \\ 0.000032 \\ 0.014074 \\ 0.014074 \\ 0.014987 \\ 0.014987 \\ 0.014852 \\ 0.014852 \\ 0.015742 \\ 0.015742 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.007263 \\ 0.036656 \\ 0.027412 \\ 0.027412 \\ 0.074416 \\ 0.024584 \\ 0.024584 \\ 0.101131 \\ 0.101131 \\ 0.10711 \\ 0.10711 \\ 0.132393 \\ 0.132393 \\ 0.13033 \\ 0.13033 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.007496 \\ 0.039525 \\ 0.041944 \\ 0.041944 \\ 0.042637 \\ 0.042943 \\ 0.042943 \\ 0.106625 \\ 0.106625 \\ 0.106699 \\ 0.106699 \\ 0.114136 \\ 0.114136 \\ 0.114464 \\ 0.114464 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.007236 \\ 0.035926 \\ 0.007771 \\ 0.024377 \\ 0.072818 \\ 0.007158 \\ 0.025066 \\ 0.01915 \\ 0.061688 \\ 0.108603 \\ 0.031905 \\ 0.121467 \\ 0.116325 \\ 0.060337 \\ 0.06111 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ -0.003804 \\ -0.020196 \\ -0.021199 \\ -0.021199 \\ -0.021861 \\ -0.02194 \\ -0.02194 \\ -0.056721 \\ -0.056721 \\ -0.056727 \\ -0.056727 \\ -0.060054 \\ -0.060054 \\ -0.060339 \\ -0.060339 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.007264 \\ 0.036721 \\ 0.010786 \\ -0.027132 \\ 0.073307 \\ 0.005044 \\ -0.023701 \\ 0.002683 \\ -0.090051 \\ 0.105974 \\ 0.050755 \\ 0.053682 \\ -0.027624 \\ 0.114151 \\ -0.1271 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0.642018 \\ -0.642018 \\ 0 \\ 0.661452 \\ -0.661452 \\ 0.850543 \\ -0.850543 \\ 0.154005 \\ -0.154005 \\ 0.488105 \\ -0.488105 \\ 0.507344 \\ -0.507344 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ -0.008173 \\ 0.00265 \\ 0 \\ -0.007816 \\ 0.002932 \\ -0.03403 \\ -0.021168 \\ 0.005674 \\ 0.031263 \\ -0.0401 \\ 0.044549 \\ -0.020267 \\ 0.023795 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0.000083 \\ 0.000064 \\ 0.000018 \\ 0.000018 \\ 0.000149 \\ 0.000012 \\ 0.000012 \\ 0.000804 \\ 0.000804 \\ 0.000747 \\ 0.000747 \\ 0.00096 \\ 0.00096 \\ 0.000745 \\ 0.000745 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.007264 \\ 0.036721 \\ 0.010786 \\ 0.027132 \\ 0.073307 \\ 0.005044 \\ 0.023701 \\ 0.002683 \\ 0.090051 \\ 0.105974 \\ 0.050755 \\ 0.053682 \\ 0.027624 \\ 0.114151 \\ 0.1271 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0.009757 \\ 0.009757 \\ 0 \\ 0.00001 \\ 0.00001 \\ 0.004733 \\ 0.004733 \\ 0.005042 \\ 0.005042 \\ 0.005013 \\ 0.005013 \\ 0.005319 \\ 0.005319 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0.008173 \\ 0.00265 \\ 0 \\ 0.007816 \\ 0.002932 \\ 0.03403 \\ 0.021168 \\ 0.005674 \\ 0.031263 \\ 0.0401 \\ 0.044549 \\ 0.020267 \\ 0.023795 \end{pmatrix} $ π
Qubit 0 ---|C1|-| |-|Gxpi2|-|Gxpi2|--- Qubit 1 ---|C0|-|Gxpi2|-| |-| |--- $ \begin{pmatrix} 1 \\ -0.975347 \\ 0.971858 \\ 0.968044e^{i0.510\pi} \\ 0.968044e^{-i0.510\pi} \\ 0.955358e^{i0.995\pi} \\ 0.955358e^{-i0.995\pi} \\ 0.954506e^{i0.495\pi} \\ 0.954506e^{-i0.495\pi} \\ 0.95308e^{i0.485\pi} \\ 0.95308e^{-i0.485\pi} \\ -0.950571 \\ 0.942455 \\ 0.938749e^{i0.510\pi} \\ 0.938749e^{-i0.510\pi} \\ 0.936924 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.047724 \\ 0.023799 \\ 0.030164e^{i0.308\pi} \\ 0.030164e^{i0.308\pi} \\ 0.098671e^{i0.284\pi} \\ 0.098671e^{i0.284\pi} \\ 0.113676e^{i0.251\pi} \\ 0.113676e^{i0.251\pi} \\ 0.129189e^{i0.350\pi} \\ 0.129189e^{i0.350\pi} \\ 0.064128 \\ 0.063334 \\ 0.079943e^{i0.172\pi} \\ 0.079943e^{i0.172\pi} \\ 0.092384 \end{pmatrix} $ $ \begin{pmatrix} 1 \\ -0.983764 \\ 0.971332 \\ 0.964042e^{i0.513\pi} \\ 0.964042e^{-i0.513\pi} \\ 0.958213e^{i0.996\pi} \\ 0.958213e^{-i0.996\pi} \\ 0.963337e^{i0.487\pi} \\ 0.963337e^{-i0.487\pi} \\ 0.944052e^{i0.487\pi} \\ 0.944052e^{-i0.487\pi} \\ -0.936803 \\ 0.942348 \\ 0.943347e^{i0.513\pi} \\ 0.943347e^{-i0.513\pi} \\ 0.936748 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.008418 \\ 0.000526 \\ 0.009928 \\ 0.009928 \\ 0.003947 \\ 0.003947 \\ 0.023895 \\ 0.023895 \\ 0.010644 \\ 0.010644 \\ 0.013768 \\ 0.000107 \\ 0.008655 \\ 0.008655 \\ 0.000176 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.047724 \\ 0.023799 \\ 0.030164 \\ 0.030164 \\ 0.098671 \\ 0.098671 \\ 0.113676 \\ 0.113676 \\ 0.129189 \\ 0.129189 \\ 0.064128 \\ 0.063334 \\ 0.079943 \\ 0.079943 \\ 0.092384 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.040489 \\ 0.056003 \\ 0.066806 \\ 0.066806 \\ 0.084567 \\ 0.084567 \\ 0.080735 \\ 0.080735 \\ 0.100258 \\ 0.100258 \\ 0.109502 \\ 0.111879 \\ 0.114461 \\ 0.114461 \\ 0.122339 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.046949 \\ 0.023117 \\ 0.015762 \\ 0.017133 \\ 0.058638 \\ 0.060169 \\ 0.080263 \\ 0.074081 \\ 0.057699 \\ 0.053052 \\ 0.060075 \\ 0.059683 \\ 0.062061 \\ 0.067281 \\ 0.08654 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ -0.024962 \\ -0.028545 \\ -0.032478 \\ -0.032478 \\ -0.04567 \\ -0.04567 \\ -0.046561 \\ -0.046561 \\ -0.048056 \\ -0.048056 \\ -0.050693 \\ -0.059267 \\ -0.063207 \\ -0.063207 \\ -0.065153 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ -0.050168 \\ 0.024194 \\ 0.024956 \\ -0.026442 \\ -0.061978 \\ -0.064848 \\ 0.085231 \\ -0.082329 \\ 0.117726 \\ -0.122273 \\ -0.069846 \\ 0.06504 \\ 0.043026 \\ -0.044344 \\ 0.09404 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 1 \\ 0 \\ 0.510258 \\ -0.510258 \\ 0.994992 \\ -0.994992 \\ 0.494627 \\ -0.494627 \\ 0.48476 \\ -0.48476 \\ 1 \\ 0 \\ 0.510357 \\ -0.510357 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ -0.005731 \\ 0.005492 \\ -0.027588 \\ 1.973029 \\ -0.024155 \\ 0.029561 \\ -0.015781 \\ 0.024235 \\ 0 \\ 0 \\ -0.022726 \\ 0.023856 \\ 0 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0.008593 \\ 0.000542 \\ 0.004142 \\ 0.004142 \\ 0.002985 \\ 0.002985 \\ 0.009209 \\ 0.009209 \\ 0.009517 \\ 0.009517 \\ 0.014589 \\ 0.000113 \\ 0.004885 \\ 0.004885 \\ 0.000188 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.050168 \\ 0.024194 \\ 0.024956 \\ 0.026442 \\ 0.061978 \\ 0.064848 \\ 0.085231 \\ 0.082329 \\ 0.117726 \\ 0.122273 \\ 0.069846 \\ 0.06504 \\ 0.043026 \\ 0.044344 \\ 0.09404 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0.002994 \\ 0.002994 \\ 0.000906 \\ 0.000906 \\ 0.007371 \\ 0.007371 \\ 0.001893 \\ 0.001893 \\ 0 \\ 0 \\ 0.00248 \\ 0.00248 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0.005731 \\ 0.005492 \\ 0.027588 \\ 1.973029 \\ 0.024155 \\ 0.029561 \\ 0.015781 \\ 0.024235 \\ 0 \\ 0 \\ 0.022726 \\ 0.023856 \\ 0 \end{pmatrix} $ π
Qubit 0 ---|Gxpi2|-| |-| |-|Gxpi2|-| |-|Gypi2|--- Qubit 1 ---| |-|Gxpi2|-|Gypi2|-| |-|Gypi2|-| |--- $ \begin{pmatrix} 1 \\ 0.971349 \\ 0.947583e^{i0.989\pi} \\ 0.947583e^{-i0.989\pi} \\ 0.944802e^{i0.974\pi} \\ 0.944802e^{-i0.974\pi} \\ 0.943618e^{i0.960\pi} \\ 0.943618e^{-i0.960\pi} \\ 0.94338e^{i0.987\pi} \\ 0.94338e^{-i0.987\pi} \\ 0.941212 \\ 0.932826e^{i0.021\pi} \\ 0.932826e^{-i0.021\pi} \\ 0.930681e^{i0.045\pi} \\ 0.930681e^{-i0.045\pi} \\ 0.926425 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.039865 \\ 0.409134e^{i0.330\pi} \\ 0.409134e^{i0.330\pi} \\ 0.07032e^{i0.111\pi} \\ 0.07032e^{i0.111\pi} \\ 0.166584e^{i0.464\pi} \\ 0.166584e^{i0.464\pi} \\ 0.511003e^{i0.394\pi} \\ 0.511003e^{i0.394\pi} \\ 0.04533 \\ 0.148045e^{i0.355\pi} \\ 0.148045e^{i0.355\pi} \\ 0.127488e^{i0.233\pi} \\ 0.127488e^{i0.233\pi} \\ 0.163061 \end{pmatrix} $ $ \begin{pmatrix} 1 \\ 0.973291 \\ 0.968023e^{i0.988\pi} \\ 0.968023e^{-i0.988\pi} \\ 0.950772e^{i0.974\pi} \\ 0.950772e^{-i0.974\pi} \\ 0.937273e^{i0.974\pi} \\ 0.937273e^{-i0.974\pi} \\ 0.923674e^{i0.988\pi} \\ 0.923674e^{-i0.988\pi} \\ 0.939531 \\ 0.932266e^{i0.014\pi} \\ 0.932266e^{-i0.014\pi} \\ 0.930983e^{i0.039\pi} \\ 0.930983e^{-i0.039\pi} \\ 0.927143 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.001942 \\ 0.020893 \\ 0.020893 \\ 0.005982 \\ 0.005982 \\ 0.040059 \\ 0.040059 \\ 0.019824 \\ 0.019824 \\ 0.001681 \\ 0.022088 \\ 0.022088 \\ 0.018857 \\ 0.018857 \\ 0.000718 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.039865 \\ 0.409134 \\ 0.409134 \\ 0.07032 \\ 0.07032 \\ 0.166584 \\ 0.166584 \\ 0.511003 \\ 0.511003 \\ 0.04533 \\ 0.148045 \\ 0.148045 \\ 0.127488 \\ 0.127488 \\ 0.163061 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.054594 \\ 0.082727 \\ 0.082727 \\ 0.101709 \\ 0.101709 \\ 0.116354 \\ 0.116354 \\ 0.128627 \\ 0.128627 \\ 0.115703 \\ 0.130602 \\ 0.130602 \\ 0.13373 \\ 0.13373 \\ 0.141072 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.038801 \\ 0.194059 \\ 0.20982 \\ 0.057521 \\ 0.067738 \\ 0.01594 \\ 0.018798 \\ 0.148 \\ 0.160066 \\ 0.042589 \\ 0.063259 \\ 0.058004 \\ 0.098261 \\ 0.076934 \\ 0.151181 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ -0.029069 \\ -0.053841 \\ -0.053841 \\ -0.05678 \\ -0.05678 \\ -0.058033 \\ -0.058033 \\ -0.058286 \\ -0.058286 \\ -0.060587 \\ -0.069537 \\ -0.069537 \\ -0.071839 \\ -0.071839 \\ -0.076422 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.040221 \\ -0.129608 \\ -0.163945 \\ -0.069484 \\ -0.07428 \\ 0.017449 \\ -0.026381 \\ -0.008904 \\ -0.054096 \\ 0.047037 \\ 0.08425 \\ 0.067861 \\ 0.110066 \\ 0.088907 \\ 0.162128 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0.989022 \\ -0.989022 \\ 0.973965 \\ -0.973965 \\ 0.960477 \\ -0.960477 \\ 0.986801 \\ -0.986801 \\ 0 \\ 0.021323 \\ -0.021323 \\ 0.045006 \\ -0.045006 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ -0.141877 \\ 1.859124 \\ -0.010597 \\ -0.006728 \\ -0.055498 \\ 1.943609 \\ -0.175376 \\ 1.821357 \\ 0 \\ 0.040353 \\ 0.043827 \\ 0.021785 \\ 0.03064 \\ 0 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0.001997 \\ 0.021342 \\ 0.021342 \\ 0.006299 \\ 0.006299 \\ 0.006747 \\ 0.006747 \\ 0.02111 \\ 0.02111 \\ 0.001788 \\ 0.0006 \\ 0.0006 \\ 0.000324 \\ 0.000324 \\ 0.000774 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.040221 \\ 0.129608 \\ 0.163945 \\ 0.069484 \\ 0.07428 \\ 0.017449 \\ 0.026381 \\ 0.008904 \\ 0.054096 \\ 0.047037 \\ 0.08425 \\ 0.067861 \\ 0.110066 \\ 0.088907 \\ 0.162128 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0.001438 \\ 0.001438 \\ 0.000129 \\ 0.000129 \\ 0.013389 \\ 0.013389 \\ 0.000738 \\ 0.000738 \\ 0 \\ 0.007537 \\ 0.007537 \\ 0.006448 \\ 0.006448 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0 \\ 0.141877 \\ 1.859124 \\ 0.010597 \\ 0.006728 \\ 0.055498 \\ 1.943609 \\ 0.175376 \\ 1.821357 \\ 0 \\ 0.040353 \\ 0.043827 \\ 0.021785 \\ 0.03064 \\ 0 \end{pmatrix} $ π
Qubit 0 ---|Gxpi2|-| |-| |-|Gypi2|-| |-| |--- Qubit 1 ---| |-|Gypi2|-|Gxpi2|-| |-|Gxpi2|-|Gxpi2|--- $ \begin{pmatrix} 1 \\ 0.970663e^{i0.669\pi} \\ 0.970663e^{-i0.669\pi} \\ 0.969071 \\ 0.941329 \\ 0.939664e^{i0.688\pi} \\ 0.939664e^{-i0.688\pi} \\ 0.932257e^{i0.688\pi} \\ 0.932257e^{-i0.688\pi} \\ 0.932138e^{i0.669\pi} \\ 0.932138e^{-i0.669\pi} \\ 0.931944 \\ 0.930898e^{i0.019\pi} \\ 0.930898e^{-i0.019\pi} \\ 0.930232e^{i0.642\pi} \\ 0.930232e^{-i0.642\pi} \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.024124e^{i0.230\pi} \\ 0.024124e^{i0.230\pi} \\ 0.042048 \\ 0.071238 \\ 0.048131e^{i0.264\pi} \\ 0.048131e^{i0.264\pi} \\ 0.135985e^{i0.193\pi} \\ 0.135985e^{i0.193\pi} \\ 0.15567e^{i0.184\pi} \\ 0.15567e^{i0.184\pi} \\ 0.048012 \\ 0.122574e^{i0.273\pi} \\ 0.122574e^{i0.273\pi} \\ 0.217404e^{i0.073\pi} \\ 0.217404e^{i0.073\pi} \end{pmatrix} $ $ \begin{pmatrix} 1 \\ 0.970418e^{i0.670\pi} \\ 0.970418e^{-i0.670\pi} \\ 0.971191 \\ 0.941055 \\ 0.939438e^{i0.683\pi} \\ 0.939438e^{-i0.683\pi} \\ 0.932687e^{i0.683\pi} \\ 0.932687e^{-i0.683\pi} \\ 0.931416e^{i0.670\pi} \\ 0.931416e^{-i0.670\pi} \\ 0.931273 \\ 0.931155e^{i0.013\pi} \\ 0.931155e^{-i0.013\pi} \\ 0.930181e^{i0.647\pi} \\ 0.930181e^{-i0.647\pi} \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.001078 \\ 0.001078 \\ 0.00212 \\ 0.000274 \\ 0.016402 \\ 0.016402 \\ 0.015185 \\ 0.015185 \\ 0.001256 \\ 0.001256 \\ 0.00067 \\ 0.017076 \\ 0.017076 \\ 0.014606 \\ 0.014606 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.024124 \\ 0.024124 \\ 0.042048 \\ 0.071238 \\ 0.048131 \\ 0.048131 \\ 0.135985 \\ 0.135985 \\ 0.15567 \\ 0.15567 \\ 0.048012 \\ 0.122574 \\ 0.122574 \\ 0.217404 \\ 0.217404 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.058052 \\ 0.058052 \\ 0.058847 \\ 0.114157 \\ 0.117378 \\ 0.117378 \\ 0.130612 \\ 0.130612 \\ 0.131792 \\ 0.131792 \\ 0.132106 \\ 0.133335 \\ 0.133335 \\ 0.134822 \\ 0.134822 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.006193 \\ 0.024064 \\ 0.040837 \\ 0.067039 \\ 0.009034 \\ 0.042207 \\ 0.030739 \\ 0.144067 \\ 0.042871 \\ 0.166165 \\ 0.044712 \\ 0.077705 \\ 0.071506 \\ 0.088286 \\ 0.264057 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ -0.029776 \\ -0.029776 \\ -0.031417 \\ -0.060463 \\ -0.062233 \\ -0.062233 \\ -0.070147 \\ -0.070147 \\ -0.070274 \\ -0.070274 \\ -0.070483 \\ -0.071605 \\ -0.071605 \\ -0.072321 \\ -0.072321 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.004966 \\ -0.023871 \\ 0.042475 \\ 0.072951 \\ 0.013204 \\ -0.05195 \\ 0.012762 \\ -0.144164 \\ 0.021397 \\ -0.158336 \\ 0.050235 \\ 0.091674 \\ 0.081655 \\ -0.02344 \\ -0.136164 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.669479 \\ -0.669479 \\ 0 \\ 0 \\ 0.688437 \\ -0.688437 \\ 0.688269 \\ -0.688269 \\ 0.669276 \\ -0.669276 \\ 0 \\ 0.019055 \\ -0.019055 \\ 0.642295 \\ -0.642295 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ -0.007732 \\ 0.002521 \\ 0 \\ 0 \\ -0.015644 \\ 0.002549 \\ -0.045996 \\ 0.019515 \\ -0.052209 \\ 0.027671 \\ 0 \\ 0.027407 \\ 0.03072 \\ -0.075072 \\ 0.066906 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0.000253 \\ 0.000253 \\ 0.002185 \\ 0.000291 \\ 0.00024 \\ 0.00024 \\ 0.000461 \\ 0.000461 \\ 0.000775 \\ 0.000775 \\ 0.00072 \\ 0.000275 \\ 0.000275 \\ 0.000054 \\ 0.000054 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.004966 \\ 0.023871 \\ 0.042475 \\ 0.072951 \\ 0.013204 \\ 0.05195 \\ 0.012762 \\ 0.144164 \\ 0.021397 \\ 0.158336 \\ 0.050235 \\ 0.091674 \\ 0.081655 \\ 0.02344 \\ 0.136164 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.000344 \\ 0.000344 \\ 0 \\ 0 \\ 0.005556 \\ 0.005556 \\ 0.005182 \\ 0.005182 \\ 0.000351 \\ 0.000351 \\ 0 \\ 0.005838 \\ 0.005838 \\ 0.004998 \\ 0.004998 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0.007732 \\ 0.002521 \\ 0 \\ 0 \\ 0.015644 \\ 0.002549 \\ 0.045996 \\ 0.019515 \\ 0.052209 \\ 0.027671 \\ 0 \\ 0.027407 \\ 0.03072 \\ 0.075072 \\ 0.066906 \end{pmatrix} $ π
Qubit 0 ---|C1|-| |-|Gypi2|-|C1|-| |-|Gxpi2|--- Qubit 1 ---|C0|-|Gxpi2|-| |-|C0|-|Gypi2|-| |--- $ \begin{pmatrix} 1 \\ 0.932375e^{i0.988\pi} \\ 0.932375e^{-i0.988\pi} \\ 0.93171 \\ 0.930714e^{i0.986\pi} \\ 0.930714e^{-i0.986\pi} \\ 0.927195 \\ 0.92616 \\ 0.924552e^{i0.970\pi} \\ 0.924552e^{-i0.970\pi} \\ 0.92371e^{i0.996\pi} \\ 0.92371e^{-i0.996\pi} \\ 0.922909e^{i0.017\pi} \\ 0.922909e^{-i0.017\pi} \\ 0.904111e^{i0.013\pi} \\ 0.904111e^{-i0.013\pi} \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.089475e^{i0.357\pi} \\ 0.089475e^{i0.357\pi} \\ 0.16213 \\ 0.147497e^{i0.306\pi} \\ 0.147497e^{i0.306\pi} \\ 0.109491 \\ 0.179819 \\ 0.102025e^{i0.101\pi} \\ 0.102025e^{i0.101\pi} \\ 0.162522e^{i0.242\pi} \\ 0.162522e^{i0.242\pi} \\ 0.208149e^{i0.221\pi} \\ 0.208149e^{i0.221\pi} \\ 0.236978e^{i0.353\pi} \\ 0.236978e^{i0.353\pi} \end{pmatrix} $ $ \begin{pmatrix} 1 \\ 0.926639e^{i0.996\pi} \\ -0.931373 \\ 0.930378e^{-i0.001\pi} \\ 0.925963e^{i0.990\pi} \\ 0.925963e^{-i0.990\pi} \\ 0.927525 \\ 0.923571 \\ 0.928311e^{i0.986\pi} \\ 0.928311e^{-i0.986\pi} \\ -0.925817 \\ 0.926639e^{-i0.996\pi} \\ 0.925509e^{i0.009\pi} \\ 0.925509e^{-i0.009\pi} \\ 0.930378e^{i0.001\pi} \\ 0.880493 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.024383 \\ 0.03412 \\ 0.00389 \\ 0.011825 \\ 0.011825 \\ 0.00033 \\ 0.002589 \\ 0.046114 \\ 0.046114 \\ 0.011529 \\ 0.003117 \\ 0.023205 \\ 0.023205 \\ 0.043076 \\ 0.043655 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.089475 \\ 0.089475 \\ 0.16213 \\ 0.147497 \\ 0.147497 \\ 0.109491 \\ 0.179819 \\ 0.102025 \\ 0.102025 \\ 0.162522 \\ 0.162522 \\ 0.208149 \\ 0.208149 \\ 0.236978 \\ 0.236978 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.136306 \\ 0.132192 \\ 0.133164 \\ 0.138252 \\ 0.138252 \\ 0.140003 \\ 0.144626 \\ 0.142784 \\ 0.142784 \\ 0.144878 \\ 0.144055 \\ 0.146105 \\ 0.146105 \\ 0.159418 \\ 0.20461 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.03556 \\ 0.036145 \\ 0.150249 \\ 0.075464 \\ 0.080532 \\ 0.101555 \\ 0.166076 \\ 0.085911 \\ 0.093841 \\ 0.109119 \\ 0.110421 \\ 0.152181 \\ 0.143798 \\ 0.09837 \\ 0.092732 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ -0.07002 \\ -0.07002 \\ -0.070733 \\ -0.071803 \\ -0.071803 \\ -0.075591 \\ -0.076708 \\ -0.078446 \\ -0.078446 \\ -0.079358 \\ -0.079358 \\ -0.080225 \\ -0.080225 \\ -0.100803 \\ -0.100803 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ -0.035025 \\ -0.041859 \\ 0.160428 \\ -0.077939 \\ -0.091537 \\ 0.11162 \\ 0.17744 \\ -0.105413 \\ -0.113449 \\ -0.125031 \\ -0.128859 \\ 0.172643 \\ 0.161644 \\ 0.139119 \\ 0.124274 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.98835 \\ -0.98835 \\ 0 \\ 0.985949 \\ -0.985949 \\ 0 \\ 0 \\ 0.970175 \\ -0.970175 \\ 0.996098 \\ -0.996098 \\ 0.016955 \\ -0.016955 \\ 0.013099 \\ -0.013099 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ -0.029028 \\ 1.971787 \\ 0 \\ -0.046249 \\ 1.95593 \\ 0 \\ 0 \\ -0.015624 \\ -0.008752 \\ -0.044402 \\ 1.95657 \\ 0.036202 \\ 0.04164 \\ 0.064083 \\ 0.067809 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0.006171 \\ 0.001075 \\ 0.001431 \\ 0.005118 \\ 0.005118 \\ 0.000355 \\ 0.0028 \\ 0.004058 \\ 0.004058 \\ 0.002279 \\ 0.003166 \\ 0.002813 \\ 0.002813 \\ 0.028639 \\ 0.02647 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.035025 \\ 0.041859 \\ 0.160428 \\ 0.077939 \\ 0.091537 \\ 0.11162 \\ 0.17744 \\ 0.105413 \\ 0.113449 \\ 0.125031 \\ 0.128859 \\ 0.172643 \\ 0.161644 \\ 0.139119 \\ 0.124274 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.008116 \\ 1.98835 \\ 0.00125 \\ 0.003713 \\ 0.003713 \\ 0 \\ 0 \\ 0.015793 \\ 0.015793 \\ 0.003902 \\ 0.000367 \\ 0.007942 \\ 0.007942 \\ 0.01185 \\ 0.013099 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0.029028 \\ 1.971787 \\ 0 \\ 0.046249 \\ 1.95593 \\ 0 \\ 0 \\ 0.015624 \\ 0.008752 \\ 0.044402 \\ 1.95657 \\ 0.036202 \\ 0.04164 \\ 0.064083 \\ 0.067809 \end{pmatrix} $ π
Qubit 0 ---|Gypi2|-|Gxpi2|-| |-|Gxpi2|-| |-|Gxpi2|-|Gypi2|-| |--- Qubit 1 ---| |-| |-|Gypi2|-| |-|Gxpi2|-| |-| |-|Gypi2|--- $ \begin{pmatrix} 1 \\ 0.952616e^{i0.988\pi} \\ 0.952616e^{-i0.988\pi} \\ 0.947962 \\ 0.932724 \\ -0.931957 \\ 0.920405e^{i0.986\pi} \\ 0.920405e^{-i0.986\pi} \\ -0.915728 \\ 0.91507e^{i0.012\pi} \\ 0.91507e^{-i0.012\pi} \\ 0.909273e^{i0.014\pi} \\ 0.909273e^{-i0.014\pi} \\ 0.909227e^{i0.997\pi} \\ 0.909227e^{-i0.997\pi} \\ 0.906751 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.068075e^{i0.265\pi} \\ 0.068075e^{i0.265\pi} \\ 0.058865 \\ 0.080615 \\ 0.116338 \\ 0.216153e^{i0.263\pi} \\ 0.216153e^{i0.263\pi} \\ 0.280259 \\ 0.241891e^{i0.177\pi} \\ 0.241891e^{i0.177\pi} \\ 0.167407e^{i0.216\pi} \\ 0.167407e^{i0.216\pi} \\ 0.403786e^{i0.316\pi} \\ 0.403786e^{i0.316\pi} \\ 0.253563 \end{pmatrix} $ $ \begin{pmatrix} 1 \\ 0.954813e^{i0.987\pi} \\ 0.954813e^{-i0.987\pi} \\ 0.946742 \\ 0.934716 \\ 0.930421e^{i0.999\pi} \\ 0.916436e^{i0.986\pi} \\ 0.916436e^{-i0.986\pi} \\ 0.930421e^{-i0.999\pi} \\ 0.912841e^{i0.011\pi} \\ 0.912841e^{-i0.011\pi} \\ 0.909862e^{i0.016\pi} \\ 0.909862e^{-i0.016\pi} \\ 0.905479e^{i0.997\pi} \\ 0.905479e^{-i0.997\pi} \\ 0.907443 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.003373 \\ 0.003373 \\ 0.00122 \\ 0.001991 \\ 0.004382 \\ 0.004052 \\ 0.004052 \\ 0.015247 \\ 0.00328 \\ 0.00328 \\ 0.004303 \\ 0.004303 \\ 0.00375 \\ 0.00375 \\ 0.000692 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.068075 \\ 0.068075 \\ 0.058865 \\ 0.080615 \\ 0.116338 \\ 0.216153 \\ 0.216153 \\ 0.280259 \\ 0.241891 \\ 0.241891 \\ 0.167407 \\ 0.167407 \\ 0.403786 \\ 0.403786 \\ 0.253563 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.090433 \\ 0.090433 \\ 0.102525 \\ 0.128168 \\ 0.132896 \\ 0.156508 \\ 0.156508 \\ 0.147996 \\ 0.164689 \\ 0.164689 \\ 0.172695 \\ 0.172695 \\ 0.176714 \\ 0.176714 \\ 0.177176 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.041938 \\ 0.045573 \\ 0.05573 \\ 0.075352 \\ 0.107765 \\ 0.128204 \\ 0.14034 \\ 0.261905 \\ 0.193991 \\ 0.180499 \\ 0.124343 \\ 0.112461 \\ 0.198319 \\ 0.201586 \\ 0.230094 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ -0.048544 \\ -0.048544 \\ -0.053441 \\ -0.069646 \\ -0.070469 \\ -0.082941 \\ -0.082941 \\ -0.088036 \\ -0.088755 \\ -0.088755 \\ -0.09511 \\ -0.09511 \\ -0.095161 \\ -0.095161 \\ -0.097888 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ -0.045518 \\ -0.05003 \\ 0.060244 \\ 0.082896 \\ -0.13334 \\ -0.142482 \\ -0.163214 \\ -0.365355 \\ 0.212295 \\ 0.205176 \\ 0.142851 \\ 0.134895 \\ -0.165881 \\ -0.174562 \\ 0.246578 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.987637 \\ -0.987637 \\ 0 \\ 0 \\ 1 \\ 0.985905 \\ -0.985905 \\ 1 \\ 0.012301 \\ -0.012301 \\ 0.014466 \\ -0.014466 \\ 0.997356 \\ -0.997356 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ -0.018211 \\ 1.98296 \\ 0 \\ 0 \\ 0 \\ -0.066327 \\ 1.937661 \\ 0 \\ 0.033811 \\ 0.038577 \\ 0.030113 \\ 0.033995 \\ -0.145464 \\ 1.854875 \\ 0 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0.002304 \\ 0.002304 \\ 0.001287 \\ 0.002132 \\ 0.001649 \\ 0.004322 \\ 0.004322 \\ 0.015918 \\ 0.002439 \\ 0.002439 \\ 0.000648 \\ 0.000648 \\ 0.00413 \\ 0.00413 \\ 0.000763 \end{pmatrix} $ ± $ \begin{pmatrix} 0 \\ 0.045518 \\ 0.05003 \\ 0.060244 \\ 0.082896 \\ 0.13334 \\ 0.142482 \\ 0.163214 \\ 0.365355 \\ 0.212295 \\ 0.205176 \\ 0.142851 \\ 0.134895 \\ 0.165881 \\ 0.174562 \\ 0.246578 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.000854 \\ 0.000854 \\ 0 \\ 0 \\ 0.001403 \\ 0.000281 \\ 0.000281 \\ 1.998597 \\ 0.000838 \\ 0.000838 \\ 0.001492 \\ 0.001492 \\ 0.000044 \\ 0.000044 \\ 0 \end{pmatrix} $ π ± $ \begin{pmatrix} 0 \\ 0.018211 \\ 1.98296 \\ 0 \\ 0 \\ 0 \\ 0.066327 \\ 1.937661 \\ 0 \\ 0.033811 \\ 0.038577 \\ 0.030113 \\ 0.033995 \\ 0.145464 \\ 1.854875 \\ 0 \end{pmatrix} $ π
Gate or Germ Eigenvalues ($E$) Target Evals. ($T$) $|E - T|$ $1.0 - \mathrm{Re}(\bar{T}\cdot E)$ $\mathrm{Re} \log(E)$ $\mathrm{Im} \log(E)$ $|\mathrm{Re}(\log E) - \mathrm{Re}(\log T)|$ $|\mathrm{Im}(\log E) - \mathrm{Im}(\log T)|$
[]$ \begin{pmatrix} 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \end{pmatrix} $ $ \begin{pmatrix} 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π
Gxpi2:1$ \begin{pmatrix} 1i \\ -1i \\ 1i \\ -1i \\ 1 \\ 1i \\ -1i \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1i \\ -1i \\ 1 \end{pmatrix} $ $ \begin{pmatrix} 1i \\ -1i \\ 1i \\ -1i \\ 1 \\ 1i \\ -1i \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1i \\ -1i \\ 1 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0.5 \\ -0.5 \\ 0.5 \\ -0.5 \\ 0 \\ 0.5 \\ -0.5 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0.5 \\ -0.5 \\ 0 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π
Gxpi2:0$ \begin{pmatrix} 1i \\ -1i \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1i \\ -1i \\ 1i \\ -1i \\ 1 \\ 1 \\ 1i \\ -1i \end{pmatrix} $ $ \begin{pmatrix} 1i \\ -1i \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1i \\ -1i \\ 1i \\ -1i \\ 1 \\ 1 \\ 1i \\ -1i \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0.5 \\ -0.5 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0.5 \\ -0.5 \\ 0.5 \\ -0.5 \\ 0 \\ 0 \\ 0.5 \\ -0.5 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π
Gypi2:1$ \begin{pmatrix} 1i \\ -1i \\ 1 \\ 1i \\ -1i \\ 1 \\ 1 \\ 1i \\ -1i \\ 1 \\ 1 \\ 1 \\ 1 \\ 1i \\ -1i \\ 1 \end{pmatrix} $ $ \begin{pmatrix} 1i \\ -1i \\ 1 \\ 1i \\ -1i \\ 1 \\ 1 \\ 1i \\ -1i \\ 1 \\ 1 \\ 1 \\ 1 \\ 1i \\ -1i \\ 1 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0.5 \\ -0.5 \\ 0 \\ 0.5 \\ -0.5 \\ 0 \\ 0 \\ 0.5 \\ -0.5 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0.5 \\ -0.5 \\ 0 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π
Gypi2:0$ \begin{pmatrix} 1i \\ -1i \\ 1i \\ -1i \\ 1 \\ 1i \\ -1i \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1i \\ -1i \\ 1 \end{pmatrix} $ $ \begin{pmatrix} 1i \\ -1i \\ 1i \\ -1i \\ 1 \\ 1i \\ -1i \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1i \\ -1i \\ 1 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0.5 \\ -0.5 \\ 0.5 \\ -0.5 \\ 0 \\ 0.5 \\ -0.5 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0.5 \\ -0.5 \\ 0 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π
Gcphase:0:1$ \begin{pmatrix} 1 \\ -1 \\ 1 \\ 1 \\ 1 \\ -1 \\ 1 \\ 1 \\ -1 \\ 1 \\ 1 \\ 1 \\ 1 \\ -1 \\ -1 \\ -1 \end{pmatrix} $ $ \begin{pmatrix} 1 \\ -1 \\ 1 \\ 1 \\ 1 \\ -1 \\ 1 \\ 1 \\ -1 \\ 1 \\ 1 \\ 1 \\ 1 \\ -1 \\ -1 \\ -1 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 1 \\ 0 \\ 0 \\ 0 \\ 1 \\ 0 \\ 0 \\ 1 \\ 0 \\ 0 \\ 0 \\ 0 \\ 1 \\ 1 \\ 1 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π
Qubit 0 ---|Gxpi2|-|Gypi2|--- Qubit 1 ---| |-| |--- $ \begin{pmatrix} 1e^{i0.667\pi} \\ 1e^{-i0.667\pi} \\ 1 \\ 1e^{i0.667\pi} \\ 1e^{-i0.667\pi} \\ 1 \\ 1 \\ 1 \\ 1e^{i0.667\pi} \\ 1e^{-i0.667\pi} \\ 1e^{i0.667\pi} \\ 1e^{-i0.667\pi} \\ 1 \\ 1 \\ 1 \\ 1 \end{pmatrix} $ $ \begin{pmatrix} 1e^{i0.667\pi} \\ 1e^{-i0.667\pi} \\ 1 \\ 1e^{i0.667\pi} \\ 1e^{-i0.667\pi} \\ 1 \\ 1 \\ 1 \\ 1e^{i0.667\pi} \\ 1e^{-i0.667\pi} \\ 1e^{i0.667\pi} \\ 1e^{-i0.667\pi} \\ 1 \\ 1 \\ 1 \\ 1 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0.666667 \\ -0.666667 \\ 0 \\ 0.666667 \\ -0.666667 \\ 0 \\ 0 \\ 0 \\ 0.666667 \\ -0.666667 \\ 0.666667 \\ -0.666667 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π
Qubit 0 ---| |-| |--- Qubit 1 ---|Gxpi2|-|Gypi2|--- $ \begin{pmatrix} 1e^{i0.667\pi} \\ 1e^{-i0.667\pi} \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1e^{i0.667\pi} \\ 1e^{-i0.667\pi} \\ 1 \\ 1e^{i0.667\pi} \\ 1e^{-i0.667\pi} \\ 1e^{i0.667\pi} \\ 1e^{-i0.667\pi} \\ 1 \\ 1 \end{pmatrix} $ $ \begin{pmatrix} 1e^{i0.667\pi} \\ 1e^{-i0.667\pi} \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1e^{i0.667\pi} \\ 1e^{-i0.667\pi} \\ 1 \\ 1e^{i0.667\pi} \\ 1e^{-i0.667\pi} \\ 1e^{i0.667\pi} \\ 1e^{-i0.667\pi} \\ 1 \\ 1 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0.666667 \\ -0.666667 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0.666667 \\ -0.666667 \\ 0 \\ 0.666667 \\ -0.666667 \\ 0.666667 \\ -0.666667 \\ 0 \\ 0 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π
Qubit 0 ---|Gxpi2|-|Gxpi2|-|Gypi2|--- Qubit 1 ---| |-| |-| |--- $ \begin{pmatrix} -1 \\ -1 \\ 1 \\ 1 \\ 1 \\ -1 \\ -1 \\ -1 \\ -1 \\ 1 \\ 1 \\ 1 \\ 1 \\ -1 \\ -1 \\ 1 \end{pmatrix} $ $ \begin{pmatrix} -1 \\ -1 \\ 1 \\ 1 \\ 1 \\ -1 \\ -1 \\ -1 \\ -1 \\ 1 \\ 1 \\ 1 \\ 1 \\ -1 \\ -1 \\ 1 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 1 \\ -1 \\ 0 \\ 0 \\ 0 \\ 1 \\ -1 \\ 1 \\ -1 \\ 0 \\ 0 \\ 0 \\ 0 \\ 1 \\ -1 \\ 0 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π
Qubit 0 ---| |-| |-| |--- Qubit 1 ---|Gxpi2|-|Gxpi2|-|Gypi2|--- $ \begin{pmatrix} -1 \\ -1 \\ 1 \\ -1 \\ -1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ -1 \\ -1 \\ -1 \\ -1 \\ 1 \\ 1 \end{pmatrix} $ $ \begin{pmatrix} -1 \\ -1 \\ 1 \\ -1 \\ -1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ -1 \\ -1 \\ -1 \\ -1 \\ 1 \\ 1 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 1 \\ -1 \\ 0 \\ 1 \\ 1 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 1 \\ -1 \\ 1 \\ -1 \\ 0 \\ 0 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π
Qubit 0 ---| |-| |-|C1|--- Qubit 1 ---|Gxpi2|-|Gypi2|-|C0|--- $ \begin{pmatrix} 1 \\ 1 \\ 1e^{i0.667\pi} \\ 1e^{-i0.667\pi} \\ 1 \\ 1e^{i0.667\pi} \\ 1e^{-i0.667\pi} \\ 1e^{i0.167\pi} \\ 1e^{-i0.167\pi} \\ 1i \\ -1i \\ 1 \\ 1i \\ -1i \\ 1e^{i0.833\pi} \\ 1e^{-i0.833\pi} \end{pmatrix} $ $ \begin{pmatrix} 1 \\ 1 \\ 1e^{i0.667\pi} \\ 1e^{-i0.667\pi} \\ 1 \\ 1e^{i0.667\pi} \\ 1e^{-i0.667\pi} \\ 1e^{i0.167\pi} \\ 1e^{-i0.167\pi} \\ 1i \\ -1i \\ 1 \\ 1i \\ -1i \\ 1e^{i0.833\pi} \\ 1e^{-i0.833\pi} \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0.666667 \\ -0.666667 \\ 0 \\ 0.666667 \\ -0.666667 \\ 0.166667 \\ -0.166667 \\ 0.5 \\ -0.5 \\ 0 \\ 0.5 \\ -0.5 \\ 0.833333 \\ -0.833333 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π
Qubit 0 ---|C1|-| |-|Gxpi2|-|Gxpi2|--- Qubit 1 ---|C0|-|Gxpi2|-| |-| |--- $ \begin{pmatrix} 1 \\ 1i \\ -1i \\ -1 \\ -1 \\ 1 \\ -1 \\ 1i \\ -1i \\ 1 \\ -1 \\ 1i \\ -1i \\ 1i \\ -1i \\ 1 \end{pmatrix} $ $ \begin{pmatrix} 1 \\ 1i \\ -1i \\ -1 \\ -1 \\ 1 \\ -1 \\ 1i \\ -1i \\ 1 \\ -1 \\ 1i \\ -1i \\ 1i \\ -1i \\ 1 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0.5 \\ -0.5 \\ 1 \\ -1 \\ 0 \\ 1 \\ 0.5 \\ -0.5 \\ 0 \\ 1 \\ 0.5 \\ -0.5 \\ 0.5 \\ -0.5 \\ 0 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π
Qubit 0 ---|Gxpi2|-| |-| |-|Gxpi2|-| |-|Gypi2|--- Qubit 1 ---| |-|Gxpi2|-|Gypi2|-| |-|Gypi2|-| |--- $ \begin{pmatrix} 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ -1 \\ -1 \\ -1 \\ -1 \\ 1 \\ -1 \\ -1 \\ -1 \\ -1 \\ 1 \\ 1 \end{pmatrix} $ $ \begin{pmatrix} 1 \\ 1 \\ 1 \\ 1 \\ 1 \\ -1 \\ -1 \\ -1 \\ -1 \\ 1 \\ -1 \\ -1 \\ -1 \\ -1 \\ 1 \\ 1 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 1 \\ -1 \\ 1 \\ -1 \\ 0 \\ 1 \\ -1 \\ 1 \\ -1 \\ 0 \\ 0 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π
Qubit 0 ---|Gxpi2|-| |-| |-|Gypi2|-| |-| |--- Qubit 1 ---| |-|Gypi2|-|Gxpi2|-| |-|Gxpi2|-|Gxpi2|--- $ \begin{pmatrix} 1 \\ 1 \\ 1 \\ 1 \\ 1e^{i0.667\pi} \\ 1e^{-i0.667\pi} \\ 1e^{i0.667\pi} \\ 1e^{-i0.667\pi} \\ 1e^{i0.667\pi} \\ 1e^{-i0.667\pi} \\ 1 \\ 1 \\ 1e^{i0.667\pi} \\ 1e^{-i0.667\pi} \\ 1e^{i0.667\pi} \\ 1e^{-i0.667\pi} \end{pmatrix} $ $ \begin{pmatrix} 1 \\ 1 \\ 1 \\ 1 \\ 1e^{i0.667\pi} \\ 1e^{-i0.667\pi} \\ 1e^{i0.667\pi} \\ 1e^{-i0.667\pi} \\ 1e^{i0.667\pi} \\ 1e^{-i0.667\pi} \\ 1 \\ 1 \\ 1e^{i0.667\pi} \\ 1e^{-i0.667\pi} \\ 1e^{i0.667\pi} \\ 1e^{-i0.667\pi} \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0.666667 \\ -0.666667 \\ 0.666667 \\ -0.666667 \\ 0.666667 \\ -0.666667 \\ 0 \\ 0 \\ 0.666667 \\ -0.666667 \\ 0.666667 \\ -0.666667 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π
Qubit 0 ---|C1|-| |-|Gypi2|-|C1|-| |-|Gxpi2|--- Qubit 1 ---|C0|-|Gxpi2|-| |-|C0|-|Gypi2|-| |--- $ \begin{pmatrix} 1 \\ 1 \\ -1 \\ -1 \\ 1 \\ 1 \\ -1 \\ -1 \\ -1 \\ -1 \\ 1 \\ 1 \\ 1 \\ -1 \\ -1 \\ 1 \end{pmatrix} $ $ \begin{pmatrix} 1 \\ 1 \\ -1 \\ -1 \\ 1 \\ 1 \\ -1 \\ -1 \\ -1 \\ -1 \\ 1 \\ 1 \\ 1 \\ -1 \\ -1 \\ 1 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 1 \\ -1 \\ 0 \\ 0 \\ 1 \\ -1 \\ 1 \\ -1 \\ 0 \\ 0 \\ 0 \\ 1 \\ -1 \\ 0 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 2 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π
Qubit 0 ---|Gypi2|-|Gxpi2|-| |-|Gxpi2|-| |-|Gxpi2|-|Gypi2|-| |--- Qubit 1 ---| |-| |-|Gypi2|-| |-|Gxpi2|-| |-| |-|Gypi2|--- $ \begin{pmatrix} 1 \\ 1 \\ -1 \\ -1 \\ 1 \\ 1 \\ 1 \\ 1 \\ -1 \\ -1 \\ -1 \\ -1 \\ -1 \\ -1 \\ 1 \\ 1 \end{pmatrix} $ $ \begin{pmatrix} 1 \\ 1 \\ -1 \\ -1 \\ 1 \\ 1 \\ 1 \\ 1 \\ -1 \\ -1 \\ -1 \\ -1 \\ -1 \\ -1 \\ 1 \\ 1 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 1 \\ -1 \\ 0 \\ 0 \\ 0 \\ 0 \\ 1 \\ -1 \\ 1 \\ -1 \\ 1 \\ -1 \\ 0 \\ 0 \end{pmatrix} $ π$ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π

Gauge Variant Error Metrics

This tab provides a variety of common (and uncommon) error metrics derived from the estimated gate set. All of these quanties are gauge-dependent, which means two things. First, they aren't directly physically measurable, so they can't map directly to observable error rates. Second, they are only as reliable (as diagnostics) inasmuch as pyGSTi is able to pick a sensible gauge (reference frame) in which to report gates. PyGSTi does this by first finding an estimate based on the data (and ignoring gauge entirely), then varying over all possible representations of those gates (gauges) to minimize a measure of the gates' implausibility (distance from the targets, combined with violation of positivity). This measure has parameters -- e.g. the weights placed on different gates -- and reports often include multiple "gauge optimizations". A dropdown menu in the sidebar allows switching between these options, and the parameters used for the currently-shown estimate are shown below it.

SPAM error metrics This table presents (gauge-variant) metrics that quantify errors in the SPAM operations -- the estimated initial state preparation[s] and POVM measurement -- with respect to the ideal target operations, A description of each metric can be found by hovering the pointer over the column header.
Prep/POVM Infidelity 1/2 Trace Distance 1/2 Diamond-Dist
ρ00.044929 ± 0.0033360.047612 ± 0.004058--
Mdefault0.075016 ± 0.0015970.07619 ± 0.0018260.122059 ± 0.004307
Prep/POVM Infidelity 1/2 Trace Distance 1/2 Diamond-Dist
ρ00.063947 ± 0.0041080.076873 ± 0.002123--
Mdefault0.071503 ± 0.0016280.074579 ± 0.0024540.077766 ± 0.003319
Prep/POVM Infidelity 1/2 Trace Distance 1/2 Diamond-Dist
ρ000--
Mdefault000
Individual gate error metrics This table presents various (gauge-variant) metrics that quantify errors in each individual estimated logic gate, with respect to the ideal target gates. Note that "Entanglement infidelity" and "Average gate infidelity" are two common definitions of process fidelity, and related by a constant dimensional factor. A description of each metric can be found by hovering the pointer over the column header.
Gate Entanglement Infidelity Avg. Gate Infidelity 1/2 Trace Distance 1/2 Diamond-Dist Non-unitary Ent. Infidelity Non-unitary Avg. Gate Infidelity
[]0.004518 ± 0.0033540.003615 ± 0.0026830.008601 ± 0.0152550.010213 ± 0.0240670.004478 ± 0.0032360.003582 ± 0.002589
Gxpi2:10.004066 ± 0.003330.003253 ± 0.0026640.008238 ± 0.0087640.011578 ± 0.0166540.004027 ± 0.0033330.003222 ± 0.002667
Gxpi2:00.00576 ± 0.0035170.004608 ± 0.0028130.020257 ± 0.0088290.027131 ± 0.0237170.005433 ± 0.0035170.004347 ± 0.002813
Gypi2:10.006353 ± 0.0048230.005083 ± 0.0038590.016997 ± 0.0088890.024357 ± 0.0252270.006157 ± 0.004760.004925 ± 0.003808
Gypi2:00.010279 ± 0.0043810.008223 ± 0.0035050.026744 ± 0.0116630.035214 ± 0.0445430.009742 ± 0.0044090.007794 ± 0.003527
Gcphase:0:10.023373 ± 0.0064430.018699 ± 0.0051540.044264 ± 0.0070590.061999 ± 0.038090.022268 ± 0.006220.017814 ± 0.004976
Gate Entanglement Infidelity Avg. Gate Infidelity 1/2 Trace Distance 1/2 Diamond-Dist Non-unitary Ent. Infidelity Non-unitary Avg. Gate Infidelity
[]0.008327 ± 0.0041180.006662 ± 0.0032940.013126 ± 0.1130070.015144 ± 0.0136370.008238 ± 0.0038360.00659 ± 0.003069
Gxpi2:10.009474 ± 0.0037280.007579 ± 0.0029830.01249 ± 0.0058670.014506 ± 0.039510.009412 ± 0.00370.007529 ± 0.00296
Gxpi2:00.008635 ± 0.0065250.006908 ± 0.005220.026421 ± 0.0073590.034333 ± 0.0436410.008121 ± 0.0063090.006496 ± 0.005047
Gypi2:10.010377 ± 0.0070770.008302 ± 0.0056620.02524 ± 0.0074160.031271 ± 0.0164470.009964 ± 0.006980.007972 ± 0.005584
Gypi2:00.010939 ± 0.0050130.008751 ± 0.0040110.028377 ± 0.0166110.036155 ± 0.0028750.010323 ± 0.0049650.008259 ± 0.003972
Gcphase:0:10.018755 ± 0.0051380.015004 ± 0.0041110.042103 ± 0.0056520.048942 ± 0.0472350.017644 ± 0.0058790.014115 ± 0.004703
Gate Entanglement Infidelity Avg. Gate Infidelity 1/2 Trace Distance 1/2 Diamond-Dist Non-unitary Ent. Infidelity Non-unitary Avg. Gate Infidelity
[]000000
Gxpi2:1000000
Gxpi2:0000000
Gypi2:1000000
Gypi2:0000000
Gcphase:0:1000000
Single metric comparison. TODO: caption
Entanglement Infidelity
Gate CPTP H+S Target
[]0.0045180.0083270
Gxpi2:10.0040660.0094740
Gxpi2:00.005760.0086350
Gypi2:10.0063530.0103770
Gypi2:00.0102790.0109390
Gcphase:0:10.0233730.0187550
Avg. Gate Infidelity
Gate CPTP H+S Target
[]0.0036150.0066620
Gxpi2:10.0032530.0075790
Gxpi2:00.0046080.0069080
Gypi2:10.0050830.0083020
Gypi2:00.0082230.0087510
Gcphase:0:10.0186990.0150040
1/2 Trace Distance
Gate CPTP H+S Target
[]0.0086010.0131260
Gxpi2:10.0082380.012490
Gxpi2:00.0202570.0264210
Gypi2:10.0169970.025240
Gypi2:00.0267440.0283770
Gcphase:0:10.0442640.0421030
1/2 Diamond-Dist
Gate CPTP H+S Target
[]0.0102130.0151440
Gxpi2:10.0115780.0145060
Gxpi2:00.0271310.0343330
Gypi2:10.0243570.0312710
Gypi2:00.0352140.0361550
Gcphase:0:10.0619990.0489420
Non-unitary Ent. Infidelity
Gate CPTP H+S Target
[]0.0044780.0082380
Gxpi2:10.0040270.0094120
Gxpi2:00.0054330.0081210
Gypi2:10.0061570.0099640
Gypi2:00.0097420.0103230
Gcphase:0:10.0222680.0176440
Non-unitary Avg. Gate Infidelity
Gate CPTP H+S Target
[]0.0035820.006590
Gxpi2:10.0032220.0075290
Gxpi2:00.0043470.0064960
Gypi2:10.0049250.0079720
Gypi2:00.0077940.0082590
Gcphase:0:10.0178140.0141150
Frobenius Distance
Gate CPTP H+S Target
[]0.0408280.0633920
Gxpi2:10.0393460.059130
Gxpi2:00.1047270.1326040
Gypi2:10.0835860.1221050
Gypi2:00.1373870.14670
Gcphase:0:10.2103130.202140
Per-germ error metrics This table presents various (gauge-variant) metrics that quantify errors in the estimated germs, with respect to their ideal target counterparts (as computed from the ideal target gates). A description of each metric can be found by hovering the pointer over the column header..
Gate or Germ Entanglement Infidelity 1/2 Trace Distance Non-unitary Ent. Infidelity
[]0.0045180.0086010.004478
Gxpi2:10.0040660.0082380.004027
Gxpi2:00.005760.0202570.005433
Gypi2:10.0063530.0169970.006157
Gypi2:00.0102790.0267440.009742
Gcphase:0:10.0233730.0442640.022268
Qubit 0 ---|Gxpi2|-|Gypi2|--- Qubit 1 ---| |-| |--- 0.0165710.0441310.015105
Qubit 0 ---| |-| |--- Qubit 1 ---|Gxpi2|-|Gypi2|--- 0.010410.0211560.010157
Qubit 0 ---|Gxpi2|-|Gxpi2|-|Gypi2|--- Qubit 1 ---| |-| |-| |--- 0.0232130.0608770.020427
Qubit 0 ---| |-| |-| |--- Qubit 1 ---|Gxpi2|-|Gxpi2|-|Gypi2|--- 0.0144630.0259710.014133
Qubit 0 ---| |-| |-|C1|--- Qubit 1 ---|Gxpi2|-|Gypi2|-|C0|--- 0.0339650.0592480.032201
Qubit 0 ---|C1|-| |-|Gxpi2|-|Gxpi2|--- Qubit 1 ---|C0|-|Gxpi2|-| |-| |--- 0.0390280.0675950.036689
Qubit 0 ---|Gxpi2|-| |-| |-|Gxpi2|-| |-|Gypi2|--- Qubit 1 ---| |-|Gxpi2|-|Gypi2|-| |-|Gypi2|-| |--- 0.0379840.0614050.036312
Qubit 0 ---|Gxpi2|-| |-| |-|Gypi2|-| |-| |--- Qubit 1 ---| |-|Gypi2|-|Gxpi2|-| |-|Gxpi2|-|Gxpi2|--- 0.0338190.0489570.032894
Qubit 0 ---|C1|-| |-|Gypi2|-|C1|-| |-|Gxpi2|--- Qubit 1 ---|C0|-|Gxpi2|-| |-|C0|-|Gypi2|-| |--- 0.070870.095740.067882
Qubit 0 ---|Gypi2|-|Gxpi2|-| |-|Gxpi2|-| |-|Gxpi2|-|Gypi2|-| |--- Qubit 1 ---| |-| |-|Gypi2|-| |-|Gxpi2|-| |-| |-|Gypi2|--- 0.0537810.0826340.05079
Gate or Germ Entanglement Infidelity 1/2 Trace Distance Non-unitary Ent. Infidelity
[]0.0083270.0131260.008238
Gxpi2:10.0094740.012490.009412
Gxpi2:00.0086350.0264210.008121
Gypi2:10.0103770.025240.009964
Gypi2:00.0109390.0283770.010323
Gcphase:0:10.0187550.0421030.017644
Qubit 0 ---|Gxpi2|-|Gypi2|--- Qubit 1 ---| |-| |--- 0.0201040.0495440.018306
Qubit 0 ---| |-| |--- Qubit 1 ---|Gxpi2|-|Gypi2|--- 0.0197760.0337470.019197
Qubit 0 ---|Gxpi2|-|Gxpi2|-|Gypi2|--- Qubit 1 ---| |-| |-| |--- 0.0298020.0708790.026249
Qubit 0 ---| |-| |-| |--- Qubit 1 ---|Gxpi2|-|Gxpi2|-|Gypi2|--- 0.0290180.041890.028266
Qubit 0 ---| |-| |-|C1|--- Qubit 1 ---|Gxpi2|-|Gypi2|-|C0|--- 0.0384310.0650430.036308
Qubit 0 ---|C1|-| |-|Gxpi2|-|Gxpi2|--- Qubit 1 ---|C0|-|Gxpi2|-| |-| |--- 0.0449740.0733810.042437
Qubit 0 ---|Gxpi2|-| |-| |-|Gxpi2|-| |-|Gypi2|--- Qubit 1 ---| |-|Gxpi2|-|Gypi2|-| |-|Gypi2|-| |--- 0.0583720.0936130.054261
Qubit 0 ---|Gxpi2|-| |-| |-|Gypi2|-| |-| |--- Qubit 1 ---| |-|Gypi2|-|Gxpi2|-| |-|Gxpi2|-|Gxpi2|--- 0.057180.0784310.054985
Qubit 0 ---|C1|-| |-|Gypi2|-|C1|-| |-|Gxpi2|--- Qubit 1 ---|C0|-|Gxpi2|-| |-|C0|-|Gypi2|-| |--- 0.0739850.100450.070663
Qubit 0 ---|Gypi2|-|Gxpi2|-| |-|Gxpi2|-| |-|Gxpi2|-|Gypi2|-| |--- Qubit 1 ---| |-| |-|Gypi2|-| |-|Gxpi2|-| |-| |-|Gypi2|--- 0.0775380.1171930.071591
Gate or Germ Entanglement Infidelity 1/2 Trace Distance Non-unitary Ent. Infidelity
[]000
Gxpi2:1000
Gxpi2:0000
Gypi2:1000
Gypi2:0000
Gcphase:0:1000
Qubit 0 ---|Gxpi2|-|Gypi2|--- Qubit 1 ---| |-| |--- 000
Qubit 0 ---| |-| |--- Qubit 1 ---|Gxpi2|-|Gypi2|--- 000
Qubit 0 ---|Gxpi2|-|Gxpi2|-|Gypi2|--- Qubit 1 ---| |-| |-| |--- 000
Qubit 0 ---| |-| |-| |--- Qubit 1 ---|Gxpi2|-|Gxpi2|-|Gypi2|--- 000
Qubit 0 ---| |-| |-|C1|--- Qubit 1 ---|Gxpi2|-|Gypi2|-|C0|--- 000
Qubit 0 ---|C1|-| |-|Gxpi2|-|Gxpi2|--- Qubit 1 ---|C0|-|Gxpi2|-| |-| |--- 000
Qubit 0 ---|Gxpi2|-| |-| |-|Gxpi2|-| |-|Gypi2|--- Qubit 1 ---| |-|Gxpi2|-|Gypi2|-| |-|Gypi2|-| |--- 000
Qubit 0 ---|Gxpi2|-| |-| |-|Gypi2|-| |-| |--- Qubit 1 ---| |-|Gypi2|-|Gxpi2|-| |-|Gxpi2|-|Gxpi2|--- 000
Qubit 0 ---|C1|-| |-|Gypi2|-|C1|-| |-|Gxpi2|--- Qubit 1 ---|C0|-|Gxpi2|-| |-|C0|-|Gypi2|-| |--- 000
Qubit 0 ---|Gypi2|-|Gxpi2|-| |-|Gxpi2|-| |-|Gxpi2|-|Gypi2|-| |--- Qubit 1 ---| |-| |-|Gypi2|-| |-|Gxpi2|-| |-| |-|Gypi2|--- 000

Raw Estimates

This tab shows the raw GST estimates — the density matrices, POVM effects, and process matrices that comprise the estimated gateset. These are explicitly gauge-dependent, and most reports include multiple gauge optimizations that correspond to slightly different (but physically equivalent and indistinguishable) representations of the operations. Usually, these raw estimates are less useful than the derived properties and decompositions shown elsewhere, but sometimes it's useful to see them. Furthermore, it's possible (at least in some versions of the report) to download the raw gateset in machine-readable form, in order to do calculations and simulations with it.

Estimated SPAM operations This table presents the GST-estimated SPAM operations — the initial state, as a density matrix, and the terminating measurement as a POVM — and compares them to the corresponding ideal target operations. All of these matrices should be positive semidefinite, so their eigenvalues are shown to provide a quick diagnostic.
Operator Target Matrix Estimated Matrix Target Eigenvals Estimated Eigenvals
ρ0
$ \begin{pmatrix} 1 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0.95524 \\ 0.02952 \\ 0.014135 \\ 0.001105 \end{pmatrix} $ ± $ \begin{pmatrix} 0.003372 \\ 0.004574 \\ 0.004103 \\ 0.002843 \end{pmatrix} $
00
$ \begin{pmatrix} 1 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0.981973 \\ 0.075582 \\ 0.034043 \\ 0.011406 \end{pmatrix} $ ± $ \begin{pmatrix} 0.003517 \\ 0.005059 \\ 0.00463 \\ 0.003248 \end{pmatrix} $
01
$ \begin{pmatrix} 0 \\ 1 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0.948419 \\ 0.075281 \\ 0.007969 \\ 0.009961 \end{pmatrix} $ ± $ \begin{pmatrix} 0.003238 \\ 0.005015 \\ 0.004419 \\ 0.002907 \end{pmatrix} $
10
$ \begin{pmatrix} 0 \\ 0 \\ 1 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0.893266 \\ 0.036566 \\ 0.007521 \\ 0.004568 \end{pmatrix} $ ± $ \begin{pmatrix} 0.003411 \\ 0.005236 \\ 0.005163 \\ 0.00343 \end{pmatrix} $
11
$ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 1 \end{pmatrix} $ $ \begin{pmatrix} 0.878734 \\ -0.000001 \\ 0.02221 \\ 0.012501 \end{pmatrix} $ ± $ \begin{pmatrix} 0.004112 \\ 0.002991 \\ 0.005177 \\ 0.005088 \end{pmatrix} $
Operator Target Matrix Estimated Matrix Target Eigenvals Estimated Eigenvals
ρ0
$ \begin{pmatrix} 1 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0.937427 \\ 0.036235 \\ 0.0186 \\ 0.007738 \end{pmatrix} $ ± $ \begin{pmatrix} 0.004092 \\ 0.006181 \\ 0.003262 \\ 0.003685 \end{pmatrix} $
00
$ \begin{pmatrix} 1 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0.927687 \\ 0.042684 \\ 0.026423 \\ 0.003206 \end{pmatrix} $ ± $ \begin{pmatrix} 0.004141 \\ 0.005683 \\ 0.005483 \\ 0.003348 \end{pmatrix} $
01
$ \begin{pmatrix} 0 \\ 1 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0.931208 \\ 0.02608 \\ 0.042712 \\ 2\times 10^{-9} \end{pmatrix} $ ± $ \begin{pmatrix} 0.003727 \\ 0.005822 \\ 0.004913 \\ 0.005182 \end{pmatrix} $
10
$ \begin{pmatrix} 0 \\ 0 \\ 1 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0.931078 \\ 0.040953 \\ 0.00064 \\ 0.027329 \end{pmatrix} $ ± $ \begin{pmatrix} 0.003293 \\ 0.00658 \\ 0.003252 \\ 0.010916 \end{pmatrix} $
11
$ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 1 \end{pmatrix} $ $ \begin{pmatrix} 0.925533 \\ 0.001502 \\ 0.045588 \\ 0.027377 \end{pmatrix} $ ± $ \begin{pmatrix} 0.006267 \\ 0.005366 \\ 0.007728 \\ 0.007726 \end{pmatrix} $
Operator Target Matrix Estimated Matrix Target Eigenvals Estimated Eigenvals
ρ0
$ \begin{pmatrix} 1 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 1 \\ 0 \\ 0 \\ 0 \end{pmatrix} $
00
$ \begin{pmatrix} 1 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 1 \\ 0 \\ 0 \\ 0 \end{pmatrix} $
01
$ \begin{pmatrix} 0 \\ 1 \\ 0 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 1 \\ 0 \\ 0 \end{pmatrix} $
10
$ \begin{pmatrix} 0 \\ 0 \\ 1 \\ 0 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 1 \\ 0 \end{pmatrix} $
11
$ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 1 \end{pmatrix} $ $ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 1 \end{pmatrix} $
Estimated logic gate operations This table presents the GST-estimated logic gates — represented as process matrices (aka Liouville superoperators or Pauli transfer matrices) — and compares them to the ideal (generally unitary) target logic gates. Each gate is represented as a d^2\times d^2 superoperator that acts by matrix multiplication on vectors in the vector space \mathcal{B}(\mathcal{H}) of operators. Matrices are displayed using a heat map that ranges between 1.0 (red) and -1.0 (blue), and hovering the pointer over a matrix element will pop up its precise numerical value. Note that it is impossible to discern even order-1%% deviations from the ideal in this view; that's what other analyses (especially the Gate Error Generators tab) are for.
Gate Target Superoperator (Tensor-product basis with components pp, pp basis) Estimated Superoperator (Tensor-product basis with components pp, pp basis) 95% C.I. half-width
[]
Gxpi2:1
Gxpi2:0
Gypi2:1
Gypi2:0
Gcphase:0:1
Gate Target Superoperator (Tensor-product basis with components pp, pp basis) Estimated Superoperator (Tensor-product basis with components pp, pp basis) 95% C.I. half-width
[]
Gxpi2:1
Gxpi2:0
Gypi2:1
Gypi2:0
Gcphase:0:1
Gate Target Superoperator (Tensor-product basis with components pp, pp basis) Estimated Superoperator (Tensor-product basis with components pp, pp basis)
[]
Gxpi2:1
Gxpi2:0
Gypi2:1
Gypi2:0
Gcphase:0:1

Gate Decompositions

This tab presents several decompositions of the process matrices shown on the Raw Estimates tab. These are derived properties of the process matrices that aren't directly interpretable as error metrics, but help understand both the overall observed/estimated behavior of the gates and how they differ from the targets. Although the tables on this page do not compare the estimated gates' properties directly to those of the ideal targets, many reports include an analysis of the target gates as well, which can be accessed (and compared directly to the GST estimates) through the Estimates dropdown menu on the sidebar. Also, since these properties are all at least mildly gauge-dependent, it may be useful to examine different gauge-optimization choices using that dropdown menu on the sidebar.

Decomposition of estimated gates. This table attempts to describe each gate as a rotation operator (this interpretation is more reliable for single qubits than for other systems). From each gate, a rotation axis and angle are extracted by considering the projection of its logarithm onto the Pauli Hamiltonian projectors. The rotation axis and angle are (respectively) given by the direction and the magnitude (up to a conventional constant) of this projected logarithm. In other words, the rotation axis is basically the Hamiltonian that generated the gate. The angles between the various gates' rotation axes are computed from the dot products between them.
Gate Ham. Evals. Rotn. angle Rotn. axis Log Error Axis angle w/[] Axis angle w/Gxpi2:1 Axis angle w/Gxpi2:0 Axis angle w/Gypi2:1 Axis angle w/Gypi2:0 Axis angle w/Gcphase:0:1
[]$ \begin{pmatrix} 0.00266 \\ 0.001147 \\ -0.002298 \\ -0.000792 \end{pmatrix} $ π0.003781π
00.470825π0.438107π0.607088π0.559357π0.329304π
Gxpi2:1$ \begin{pmatrix} 0.247197 \\ 0.248756 \\ 0.250812 \\ 0.252435 \end{pmatrix} $ π0.499616π
00.470825π0.501024π0.500168π0.499391π0.501865π
Gxpi2:0$ \begin{pmatrix} 0.253884 \\ 0.248581 \\ -0.253015 \\ -0.249917 \end{pmatrix} $ π0.502717π
00.438107π0.501024π0.497802π0.497077π0.494976π
Gypi2:1$ \begin{pmatrix} 0.252108 \\ 0.247787 \\ -0.251711 \\ -0.248462 \end{pmatrix} $ π0.500049π
00.607088π0.500168π0.497802π0.496973π0.503605π
Gypi2:0$ \begin{pmatrix} -0.248525 \\ -0.252731 \\ 0.252367 \\ 0.250096 \end{pmatrix} $ π0.501872π
00.559357π0.499391π0.497077π0.496973π0.490045π
Gcphase:0:1$ \begin{pmatrix} 0.593593 \\ -0.591931 \\ 0.105673 \\ -0.111969 \end{pmatrix} $ π0.852314π
00.329304π0.501865π0.494976π0.503605π0.490045π
Gate Ham. Evals. Rotn. angle Rotn. axis Log Error Axis angle w/[] Axis angle w/Gxpi2:1 Axis angle w/Gxpi2:0 Axis angle w/Gypi2:1 Axis angle w/Gypi2:0 Axis angle w/Gcphase:0:1
[]$ \begin{pmatrix} 0.003348 \\ -0.003917 \\ 0.000431 \\ -0.001474 \end{pmatrix} $ π0.005377π
00.549453π0.399814π0.553346π0.495403π0.281286π
Gxpi2:1$ \begin{pmatrix} 0.246806 \\ 0.252906 \\ 0.25054 \\ 0.24964 \end{pmatrix} $ π0.499965π
00.549453π0.500788π0.500055π0.499253π0.502075π
Gxpi2:0$ \begin{pmatrix} 0.257141 \\ 0.250655 \\ -0.257142 \\ -0.251529 \end{pmatrix} $ π0.50827π
00.399814π0.500788π0.495675π0.495578π0.49534π
Gypi2:1$ \begin{pmatrix} 0.253608 \\ 0.24795 \\ -0.252596 \\ -0.249065 \end{pmatrix} $ π0.501632π
00.553346π0.500055π0.495675π0.494774π0.503258π
Gypi2:0$ \begin{pmatrix} 0.256245 \\ 0.249399 \\ -0.251106 \\ -0.253576 \end{pmatrix} $ π0.50519π
00.495403π0.499253π0.495578π0.494774π0.4906π
Gcphase:0:1$ \begin{pmatrix} 0.59068 \\ -0.592674 \\ 0.108027 \\ -0.109364 \end{pmatrix} $ π0.850762π
00.281286π0.502075π0.49534π0.503258π0.4906π
Gate Ham. Evals. Rotn. angle Rotn. axis Log Error Axis angle w/[] Axis angle w/Gxpi2:1 Axis angle w/Gxpi2:0 Axis angle w/Gypi2:1 Axis angle w/Gypi2:0 Axis angle w/Gcphase:0:1
[]$ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \end{pmatrix} $ π0π
0----------
Gxpi2:1$ \begin{pmatrix} 0.25 \\ 0.25 \\ 0.25 \\ 0.25 \end{pmatrix} $ π0.5π
0--0.5π0.5π0.5π0.5π
Gxpi2:0$ \begin{pmatrix} 0.25 \\ 0.25 \\ -0.25 \\ -0.25 \end{pmatrix} $ π0.5π
0--0.5π0.5π0.5π0.5π
Gypi2:1$ \begin{pmatrix} -0.25 \\ 0.25 \\ 0.25 \\ -0.25 \end{pmatrix} $ π0.5π
0--0.5π0.5π0.5π0.499975π
Gypi2:0$ \begin{pmatrix} -0.25 \\ 0.25 \\ -0.25 \\ 0.25 \end{pmatrix} $ π0.5π
0--0.5π0.5π0.5π0.5π
Gcphase:0:1$ \begin{pmatrix} -0.603558 \\ 0.603556 \\ -0.103557 \\ 0.103558 \end{pmatrix} $ π0.866031π
0.005654--0.5π0.5π0.499975π0.5π
Estimated gates' Choi representation and spectra These plots show each gate's Choi-Jamiolkowski representation and that representation's eigenvalues. Every completely positive (CP) map has a non-negative Choi spectrum, so any negative eigenvalues (shown in red) indicate that the estimate violates positivity. If a gate is perfectly unitary, its Choi spectrum will be rank-1, and real-world gates often have many Choi eigenvalues that are very close to zero. Therefore, although negative eigenvalues indicate that the estimate is non-physical, this can easily stem from statistical fluctuations. If statistically significant, though, it usually indicates either non-Markovianity or a failed gauge optimization. Since the Choi matrix is Hermitian, it is displayed using colored boxes by placing the real and imaginary parts of the upper-triangle's off-diagonal elements in the upper and lower triangles of the color box plot, respectively.
Gate Choi matrix (Tensor-product basis with components pp, pp basis) Eigenvalue Magnitudes
[]
Gxpi2:1
Gxpi2:0
Gypi2:1
Gypi2:0
Gcphase:0:1
Gate Choi matrix (Tensor-product basis with components pp, pp basis) Eigenvalue Magnitudes
[]
Gxpi2:1
Gxpi2:0
Gypi2:1
Gypi2:0
Gcphase:0:1
Gate Choi matrix (Tensor-product basis with components pp, pp basis) Eigenvalue Magnitudes
[]
Gxpi2:1
Gxpi2:0
Gypi2:1
Gypi2:0
Gcphase:0:1

Gate Error Generators

This tab presents the error generators for each of the estimated gates. Although these are not especially well-known in the literature, they are (in the pyGSTi authors' opinion) the most useful detailed diagnostic for gate errors. The error generator \mathbb{L} for a noisy gate G with ideal target G_0 is defined by writing G = e^{\mathbb{L}} G_0 . It can be thought of, more or less, as a Lindbladian superoperator that generates the error in the gate — with two caveats. First, it is not necessarily of strict Lindblad form, because the GST-estimated gates may not be CP, and because even if they are, not every CP map is "divisible" (and nondivisible maps are not generated by Lindblad evolution). Second, the generator reported here is a post-gate generator, so it answers the question "If all the noise occurred after the ideal gate, what Lindbladian would generate it?" Finally: the error generators are very definitely gauge-dependent, so caveat emptor (cross-validating any inferences drawn from these generators with some sort of gauge-invariant diagnostic is highly recommended).

Logic gate error generators The first column displays a heat map of the estimated error generator for each gate. This is (more or less) the Lindbladian \mathbb{L} that describes how the gate is failing to match the target. This error generator is defined by the equation G = e^{\mathbb{L}} G_0 . If it is zero, the estimated gate matches the corresponding ideal target gate. Note that the range of the color scale is dynamically adjusted. Subsequent columns show the result of projecting each generator onto some subspaces of the error generator space. Each corresponds to a different classes of well-known errors: Hamiltonian (coherent) errors, Pauli-stochastic errors, and affine (aka non-unital) errors. The Hamiltonian generators act by commutation with each Pauli basis element B_i, that is \rho \rightarrow -i[B_i, \rho]. Stochastic generators act by conjugation with each basis element, \rho \rightarrow B_i \rho B_i^\dagger. Affine generators act by projecting everything onto a particular basis element, \rho \rightarrow \mathrm{Tr}(\rho) B_i. Roughly speaking, the Hamiltonian projection corresponds precisely to the Hamiltonian that would produce the coherent part of the error, while the Pauli-stochastic generators correspond to the rates of all the Pauli errors (e.g., X errors, Z errors, their 2-qubit counterparts, or whatever is appropriate for the system being analyzed).
Gate Error Generator Hamiltonian Projections Stochastic Projections Active\Correlation Projections
[]
Gxpi2:1
Gxpi2:0
Gypi2:1
Gypi2:0
Gcphase:0:1
Gate Error Generator Hamiltonian Projections Stochastic Projections Active\Correlation Projections
[]
Gxpi2:1
Gxpi2:0
Gypi2:1
Gypi2:0
Gcphase:0:1
Gate Error Generator Hamiltonian Projections Stochastic Projections Active\Correlation Projections
[]
Gxpi2:1
Gxpi2:0
Gypi2:1
Gypi2:0
Gcphase:0:1

Input Summary

This tab presents a grab bag of potentially-useful information about the target gate set and the data set(s).

Ideal SPAM operations The ideal target state preparations (\rho_i) and POVM effects E_i for the device analyzed in this report. SPAM (state preparation and measurement) operations are given as d\times d matrices in the standard (matrix unit) basis of Hilbert space.
Operator Matrix Eigenvals
ρ0
$ \begin{pmatrix} 1 \\ 0 \\ 0 \\ 0 \end{pmatrix} $
00
$ \begin{pmatrix} 1 \\ 0 \\ 0 \\ 0 \end{pmatrix} $
01
$ \begin{pmatrix} 0 \\ 1 \\ 0 \\ 0 \end{pmatrix} $
10
$ \begin{pmatrix} 0 \\ 0 \\ 1 \\ 0 \end{pmatrix} $
11
$ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 1 \end{pmatrix} $
Operator Matrix Eigenvals
ρ0
$ \begin{pmatrix} 1 \\ 0 \\ 0 \\ 0 \end{pmatrix} $
00
$ \begin{pmatrix} 1 \\ 0 \\ 0 \\ 0 \end{pmatrix} $
01
$ \begin{pmatrix} 0 \\ 1 \\ 0 \\ 0 \end{pmatrix} $
10
$ \begin{pmatrix} 0 \\ 0 \\ 1 \\ 0 \end{pmatrix} $
11
$ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 1 \end{pmatrix} $
Operator Matrix Eigenvals
ρ0
$ \begin{pmatrix} 1 \\ 0 \\ 0 \\ 0 \end{pmatrix} $
00
$ \begin{pmatrix} 1 \\ 0 \\ 0 \\ 0 \end{pmatrix} $
01
$ \begin{pmatrix} 0 \\ 1 \\ 0 \\ 0 \end{pmatrix} $
10
$ \begin{pmatrix} 0 \\ 0 \\ 1 \\ 0 \end{pmatrix} $
11
$ \begin{pmatrix} 0 \\ 0 \\ 0 \\ 1 \end{pmatrix} $
Fiducial circuits A list of the preparation and measurement fiducial circuits. These circuits precede and follow, respectively, the potentially long germ-to-some-power portion of GST gate sequences, and generate informationally complete input/output ensembles from the native state preparation[s] and measurement.
Fiducials
# Prep. Measure
1
2Gxpi2:1Gxpi2:1
3Gypi2:1Gypi2:1
4Gxpi2:1.Gxpi2:1Gxpi2:1.Gxpi2:1
5Gxpi2:0Gxpi2:0
6Gxpi2:0.Gxpi2:1Gypi2:0
7Gxpi2:0.Gypi2:1Gxpi2:0.Gxpi2:0
8Gxpi2:0.Gxpi2:1.Gxpi2:1Gxpi2:0.Gxpi2:1
9Gypi2:0Gxpi2:0.Gypi2:1
10Gypi2:0.Gxpi2:1Gypi2:0.Gxpi2:1
11Gypi2:0.Gypi2:1Gypi2:0.Gypi2:1
12Gypi2:0.Gxpi2:1.Gxpi2:1
13Gxpi2:0.Gxpi2:0
14Gxpi2:0.Gxpi2:0.Gxpi2:1
15Gxpi2:0.Gxpi2:0.Gypi2:1
16Gxpi2:0.Gxpi2:0.Gxpi2:1.Gxpi2:1
Germs A list of the germ circuits used in this experiment. Germs are relatively short circuits that get repeated (perhaps many times) in order to amplify various types of qubit errors. The list of germs is often chosen so that all possible types of in-model errors are amplified by at least one germ. Note: it's generally impossible to find a single germ that amplifies all possible errors, except when the gate being studied is the identity operation.
# Germ # Germ
1[]9Gxpi2:0.Gxpi2:0.Gypi2:0
2Gxpi2:010Gxpi2:1.Gxpi2:1.Gypi2:1
3Gypi2:011Gxpi2:1.Gypi2:1.Gcphase:0:1
4Gxpi2:112Gcphase:0:1.Gxpi2:1.Gxpi2:0.Gxpi2:0
5Gypi2:113Gxpi2:0.Gxpi2:1.Gypi2:1.Gxpi2:0.Gypi2:1.Gypi2:0
6Gcphase:0:114Gxpi2:0.Gypi2:1.Gxpi2:1.Gypi2:0.Gxpi2:1.Gxpi2:1
7Gxpi2:0.Gypi2:015Gcphase:0:1.Gxpi2:1.Gypi2:0.Gcphase:0:1.Gypi2:1.Gxpi2:0
8Gxpi2:1.Gypi2:116Gypi2:0.Gxpi2:0.Gypi2:1.Gxpi2:0.Gxpi2:1.Gxpi2:0.Gypi2:0.Gypi2:1
Dataset properties This table lists various properties of the data set used in the analysis. It is useful for sanity checks.
Quantity Value
Number of strings1702
Gate labelsGxpi2:1, Gypi2:1, Gxpi2:0, Gypi2:0, Gcphase:0:1
Outcome labels('00',), ('01',), ('10',), ('11',)
Counts per string500
User comment 1
Ideal logic gates The ideal target (generally unitary) logic gates. Each has a name starting with G, and is represented as a d^2\times d^2 superoperator that acts by matrix multiplication on vectors in \mathcal{B}(\mathcal{H}). Matrices are displayed using a heat map that ranges between 1.0 (red) and -1.0 (blue).
Gate Superoperator (Tensor-product basis with components pp, pp basis)
[]
Gxpi2:1
Gxpi2:0
Gypi2:1
Gypi2:0
Gcphase:0:1
Gate Superoperator (Tensor-product basis with components pp, pp basis)
[]
Gxpi2:1
Gxpi2:0
Gypi2:1
Gypi2:0
Gcphase:0:1
Gate Superoperator (Tensor-product basis with components pp, pp basis)
[]
Gxpi2:1
Gxpi2:0
Gypi2:1
Gypi2:0
Gcphase:0:1

System and pyGSTi parameters

This tab contains a raw dump of system information and various pyGSTi parameters. Its purpose is to stamp this report with parameters that indicate how exactly GST was run to create it, as well as to record the software environment in within which the report creation was run. However, if the core GST computation was done on a different computer, then the software information contained here will be less useful (it describes the environment in which the report was generated, not the one in which the estimate was generated).

Listing of GST parameters and meta-data. These parameters and related metadata describe how the GST computation that produced this report was performed.
Quantity Value
final_mdc_storeNone
final_objfnNone
final_objfn_builder
final_objfn_cacheNone
protocol
Quantity Value
final_mdc_storeNone
final_objfnNone
final_objfn_builder
final_objfn_cacheNone
protocol
Quantity Value
final_mdc_storeNone
final_objfnNone
final_objfn_builder
final_objfn_cacheNone
model_test_values[303924.1791762151, 387138.0523944685, 537975.3913354212, 737897.5922673217]
protocolNone
raw_objective_values[151962.08958810754, 193569.02619723426, 268987.6956677106, 368948.7961336608]
Profiler timing. Timing information from pyGSTi's built-in lightweight profiler (if it was enabled).
Label Time (sec)
Label Time (sec)
Label Time (sec)
Standard output. The standard output text, along with warnings and errors, that was collected (recorded) when GST was run to create the results reported here.
  • WWW WARNING: Treating result as *converged* after maximum iterations (100) were exceeded.
  • WWW WARNING: Treating result as *converged* after maximum iterations (100) were exceeded.
  • WWW WARNING: Treating result as *converged* after maximum iterations (100) were exceeded.
  • Iterative GST: [##################################################] 100.0% 1702 circuits
  • Iterative GST Total Time: 815.2s
  • WWW WARNING: Treating result as *converged* after maximum iterations (100) were exceeded.
  • WWW WARNING: Treating result as *converged* after maximum iterations (100) were exceeded.
  • WWW WARNING: Treating result as *converged* after maximum iterations (100) were exceeded.
  • WWW WARNING: Treating result as *converged* after maximum iterations (100) were exceeded.
  • Iterative GST: [##################################################] 100.0% 1702 circuits
  • Iterative GST Total Time: 219.6s
  • No standard output recorded
Listing of the software environment. This table describes the software environment of the machine used to generate this report. It may not describe the machine used to perform the core GST gate set estimation.
Quantity Value
pyGSTi version0.9.11.1.post2
numpy1.25.0
scipy1.11.4
matplotlib3.6.3
ply3.11
cvxopt1.3.2
cvxpy1.4.1
nosemissing
PIL10.0.0
psutil5.9.5
Python version3.10.12
Python typeCPython
Python compilerGCC 12.3.0
Python build('main', 'Jun 23 2023 22:40:32')
Python branch
Python revision
Platform summaryLinux-5.4.0-155-generic-x86_64-with-glibc2.31
SystemLinux
Sys Release5.4.0-155-generic
Sys Version#172-Ubuntu SMP Fri Jul 7 16:10:02 UTC 2023
Machinex86_64
Processorx86_64

How to use this report

Welcome to a pyGSTi report! This HTML document provides an interactive view onto a lot of information about one or more gateset tomography (GST) experiments that were analyzed using the pyGSTi software. This Help tab should help you use this report's interactive features, figure out where to find things, and access the context-sensitive help features embedded throughout the report.

Background

PyGSTi's primary purpose is to ingest GST datasets and find a good estimate of the gateset that generated that data. But pyGSTi can also produce a lot of detailed analyses and visualizations of the estimates that it generates. That's what you'll find in this report. You can inspect the raw estimated gateset too, but if you want to do your own calculations with it — e.g., to simulate experiments or calculate interesting quantities that the pyGSTi authors haven't thought of — then the best way to do that is by using pyGSTi itself in a Jupyter or iPython notebook.

This report's structure

PyGSTi uses HTML for reporting because it's pretty portable and supports interactivity. Interactivity makes it possible to embed a lot of different perspectives and analyses, without overwhelming you with too much information at once or requiring you to scroll through long static (e.g. PDF) documents. In this report, actual content is displayed in the main panel, while navigation tools that let you decide what content to examine are collected in a sidebar on the left. The tables and figures in the main panel are also somewhat interactive (see “Interacting with content” below). Most of them dynamically change what they show depending on the positions of one or more switches - dropdown-menus, button-sets, or sliders. Most switches are located on the sidebar, but some appear in the main panel beneath the figure or table that they control. Note that some content is generated on the fly, so there may be a lag the very first time you view a given tab, while your browser makes plots or renders math formulas.

Choosing what to see via the sidebar

The sidebar provides two distinct ways to control what you see. First, the data analysis is broken up into different tabs that are listed on the sidebar. Use the sidebar to hop between them. Each tab collects a particular category of analysis, presented as tables and figures. Second, if the report contains multiple analyses, the sidebar displays switches that allow you to pick which analysis to display in the main panel. A report can contain: (1) multiple distinct datasets; (2) the results of different estimators (each associated with a given dataset); and (3) multiple distinct but equivalent representations (gauges) for each estimate. You can choose between these options using the drop down menus labeled Dataset and Estimate, and the Gauge-Opt. button group at the bottom of the sidebar. If a switch is missing, the report doesn't contain multiple options of that type. You can hide the sidebar (or make is sticky) by clicking the ⊛ symbol in its upper right corner.

Due to the large amount of data a report can contain, there are options that allow one to omit some of the (usually larger or more data-dense) figures from the report at its creation time. This will result in the report having fewer tabs in the sidebar and/or the word OMITTED being displayed instead of a figure. To see missing tabs or omitted figures, you should ask whoever generated this report to re-generate it with a lower brevity setting.

Interacting with content

Each tab presents a (hopefully manageable) amount of content arranged into objects — figures and tables — that have some interactive properties. Here are some general tips and rules.

  • Resizing: Each object can be resized by dragging its lower right corner.
  • Zooming: You can zoom in on plots' axes by clicking and dragging within the figure. Double-clicking, or tapping the house icon that pops up in the upper right when the pointer is over a figure, will reset the axes.
  • Exporting: Plots can be saved in PNG format by tapping the camera icon, which only appears when the pointer is over a plot). (User beware: this is a builtin feature of the Plotly library, and we find that sometimes the saved PNG does not look like the original plot, especially in aspect ratio.) Depending on what options were selected when the report was constructed, there may also be links to download plots and tables as PDF, Python pickle files, and/or LaTeX (tables only). Plots will have additional download icons next to the camera icon, and tables will have PDF, PKL, and/or TEX links beneath them. PKL files downloaded from plots contain a pickled dictionary of the plotted data, while those downloaded from tables contain a pickled Pandas DataFrame object.
  • Full descriptive captions for figures and tables can be revealed by clicking on the object's Figure XX or Table XX title.
  • Hovering over a colored bar or box will often reveal a tool tip showing the exact number that bar or box represents. Hovering over table headings will bring up descriptive text. In the plots that show per-sequence model violation, hovering over any data point will bring up fairly extensive details about the datum that generated it.
  • Clickable pigs: If you see the pyGSTi logo, it's a placeholder for a plot that wasn't automatically generated (usually because this might take a little while); click on the logo to generate the plot.
The example table below demonstrates some of this functionality.

Click this title to see my full caption. This is an example table which demonstrates some of the functionality found in the other tables and figures of this report. Hovering over the column headers displays descriptive tooltips, and clicking on the pyGSTi logo will cause a plot to be generated. Hovering over the colored boxes of the plot will display the value of that box, potentially with additional information (in this case, error bars). Math formulas like \sqrt{x^2 + y^2} = \frac{1}{4} can be displayed in captions but not in tooltips, so sometimes the column-header tooltips simply refer to material in the captions.
Hover over me... And me! Click the pig
Pi3.141593

Quick guide to Datasets, Estimates, and Gauge Optimizations

The single biggest change from the old PDF report format is the ability to report simultaneously on — and compare — multiple gateset estimates. This report may contain an unlimited number of distinct gatesets. Although they're often all derived from the same dataset, they may not be. For example, a single report could contain:

  1. datasets from separate GST experiments on each qubit on a chip;
  2. datasets from two identical GST experiments done at different times;
  3. datasets from GST experiments on the same system, but with gate implementations;
  4. a 2-qubit GST dataset together with 1-qubit GST datasets extracted from it;
  5. many other possibilities.

The sidebar's Dataset dropdown menu (if present) lets you select a dataset. Then, the Estimate dropdown (if present) will list all the different estimates that are available for any of the datasets in the report. If you choose an estimate that was not generated for the current dataset (but is listed because it was generated for another dataset), unavailable plots and figures will turn into big "N/A" labels. Different estimates are usually generated by different statistical estimators. PyGSTi usually provides maximum likelihood estimates (although others are certainly possible!), but it can do MLE with no constraints at all (Full), or constrained to trace-preserving maps (TP), or constrained to completely positive maps (CPTP). Some reports include separate *.robust variations of those estimators in which poorly-fit data were deprecated, and some reports include the target gates themselves (Target) as an option.

Finally, in order to analyze each estimated gateset, pyGSTi has to choose a representation — a gauge — for it. Since pyGSTi does this gauge-fixing internally by defining an objective function and then finding the gauge that optimizes it, the choice-of-representation is referred to as Gauge Optimization. A description of the objective function used to generate this gateset appears at the bottom of the sidebar. If the report contains multiple gauge optimizations, you can choose between them by pushing the appropriate button. Choosing a good gauge is hard, and neither pyGSTi nor its users always get it right. If something reported in the Summary or Gauge-dependent error metrics tabs looks startling or implausible, it might be due to a poorly chosen gauge. Try a different gauge-optimization choice, or cross-validate whatever you see against things from the Gauge-invariant error metrics tabs.

What to look at first (and second)

If you're new to pyGSTi reports, this is probably all a bit overwhelming. Don't panic! There's a lot of context-sensitive help, and the pyGSTi authors are always happy to answer questions like What does this mean?, or Why would I care about this? But since these reports do contain a lot of stuff, here's a get-started-quickly guide.

Start with the Summary tab. It will tell you two critical things. First, in Table 3: how close do the gates seem to be to the ideal targets that were specified? Are you doing pretty well, or all messed up for some reason? If whoever did the analysis chose to produce error bars (this can take a lot of computation), they'll appear in this table. Second, the model violation plots will tell you whether the system seems to be stable and Markovian, or not (in which case, take the metrics in Table 3 with a grain of salt). Don't forget to flip through the available datasets, estimates, and gauge-optimization choices — or at least the ones you care about — while looking at this tab.

Next, you probably want to know one of two things. Either the GST model was NOT badly violated, in which case you want to know more about the errors in the gates.. or it WAS badly violated, in which case you want to know more about what's going wrong.

If you want to know more about the errors, start with Gauge Dependent Error Metrics: Overview, then take a quick look at Raw Estimates to confirm that the process matrices look about right, and then spend some quality time with Gate Decompositions and Gate Error Generators if you want to really understand what GST thinks that each individual gate is doing. If at any point you see something weird that might be due to a bad choice of gauge (examples include wildly nonpositive SPAM operations, implausibly high diamond norm errors in gates that you strongly believe to be better than that, and significantly negative elements in the Pauli stochastic part of the error generators), try a different gauge optimization. Or, go to the Gauge-invariant error metrics tabs and try to figure out whether there's something here that confirms or denies whatever effect is bugging you (e.g., if an estimated gate has an eigenvalue bigger than 1, that will produce crazy negative probabilities, and it's not a gauge problem).

On the other hand, if there's a lot of model violation, then you probably want to understand why. The information on the error metrics tabs may or may not be useful — you should be much more cautious about drawing conclusions from them if there's a lot of model violation. To dig into model violation (aka “non-Markovianity”), start with the Model Violation: Overview tab, which will give you the numbers behind the bar chart from the Summary tab, and also show you whether longer circuits violate the GST model more. (If they do, it's probably non-Markovianity in the gates. If they don't, it's probably something nastier like bistability, slow drift in SPAM operations, or corrupted data). Next, take a deep breath and dig into the “Per-sequence detail” tab, which will show you the (quantitative) inconsistency of every individual circuit with this estimate. Interpreting these charts is a bit of an art, but clusters of red boxes usually indicate that something related to the location of the cluster was suffering drift and/or non-Markovianity.

No message